**Engineering Mechanics Statics and Dynamics 15th EditionR. C. HibbelerCONTENTSGeneral PrinciplesChapter ObjectivesJ Mechanics. Fundamental ConceptsUnits of Measurement. The International System of Units. Numerical Calculations. General Procedure for AnalysisForce VectorsChapter Objectives. Scalars and Vectors. Vector Operations. Vector Addition of Forces. Addition of a System of CoplanarForces. Cartesian Vectors. Addition of Cartesian Vectors. Position Vectors. Force Vector Directed Along a Line. Dot ProductXIIIXIV ContentsEquilibrium of aParticle aiChapter Objectives. Condition for the Equilibriumof a Particle. The Free-Body Diagram. Coplanar Force Systems. Three-Dimensional Force SystemsForce SystemResultantsChapter Objectives. Moment of a Force—ScalarFormulation. Principle of Moments. Cross Product. Moment of a Force—VectorFormulation. Moment of a Force about aSpecified Axis. Moment of a Couple. Simplification of a Force and CoupleSystem. Further Simplification of a Force andCouple System. Reduction of a Simple DistributedLoading Contents xvEquilibrium of aRigid BodyChapter Objectives. Conditions for Rigid-BodyEquilibrium. Free-Body DiagramsEquations of Equilibrium. Two- and Three-Force Members. Free-Body Diagrams. Equations of Equilibrium. Constraints and Statical Determinacy**

**Structural AnalysisChapter Objectives. Simple Trusses. The Method of Joints. Zero-Force Members. The Method of Sections. Space Trusses. Frames and Machines XVI ContentsInternal ForcesChapter Objectives. Internal Loadings. Shear and Moment Equations andDiagrams**

**Relations among Distributed Load, Shear,**

and Moment

. Cables

Friction i

Chapter Objectives

. Characteristics of Dry Friction

. Problems Involving Dry Friction

. Wedges

. Frictional Forces on Screws

. Frictional Forces on Flat Belts

. Frictional Forces on Collar Bearings, Pivot

Bearings, and Disks

. Frictional Forces on Journal Bearings

. Rolling Resistance Contents xvii

Center of Gravity and

Centroid

Chapter Objectives

J Center of Gravity, Center of Mass, and the

Centroid of a Body

. Composite Bodies

. Theorems of Pappus and Guldinus

. Resultant of a General Distributed

Loading

. Fluid Pressure

Moments of Inertia

Chapter Objectives

. Definition of Moments of Inertia for

Areas

. Parallel-Axis Theorem for an Area

. Radius of Gyration of an Area

. Moments of Inertia for Composite

Areas

. Product of Inertia for an Area

. Moments of Inertia for an Area about

Inclined Axes

. Mohr’s Circle for Moments of Inertia

. Mass Moment of Inertia XVIII Contents

Virtual Work

Chapter Objectives- Definition of Work
- Principle of Virtual Work
- Principle of Virtual Work for a System of

Connected Rigid Bodies - Conservative Forces
- Potential Energy
- Potential-Energy Criterion for

Equilibrium **Stability of Equilibrium Configuration**

Appendix

A* Mathematical Review and

Formulations

Fundamental Problem

Solutions and

Answers

Review Problem

Answers

Selected Answers

Index Contents xix

Kinematics of a

Particle

Chapter Objectives

. Introduction

. Rectilinear Kinematics: Continuous

Motion

. Rectilinear Kinematics: Erratic Motion

. General Curvilinear Motion

. Curvilinear Motion: Rectangular

Components

. Motion of a Projectile

. Curvilinear Motion: Normal and Tangential

Components- . Curvilinear Motion: Cylindrical

Components - Absolute Dependent Motion Analysis of

Two Particles

. Relative Motion of Two Particles Using

Translating Axes

Kinetics of

a Particle: Force and

Acceleration

Chapter Objectives

. Newton’s Second Law of Motion

. The Equation of Motion

. Equation of Motion for a System of

Particles

. Equations of Motion: Rectangular

Coordinates

. Equations of Motion: Normal and

Tangential Coordinates

- . Equations of Motion: Cylindrical

Coordinates - . Central-Force Motion and Space

Mechanics XX Contents

Kinetics of a Particle:

Work and Energy

Chapter Objectives

. The Work of a Force

. Principle of Work and Energy

. Principle of Work and Energy for a System

of Particles

. Power and Efficiency

. Conservative Forces and Potential

Energy

. Conservation of Energy

Kinetics of a

Particle: Impulse

and Momentum

Chapter Objectives

. Principle of Linear Impulse and

Momentum

. Principle of Linear Impulse and Momentum

for a System of Particles

. Conservation of Linear Momentum for a

System of Particles

. Impact

. Angular Momentum

. Relation Between the Moment of a Force

and Angular Momentum

. Principle of Angular Impulse and

Momentum

. Bodies Subjected to a Mass Flow

. Steady Flow of a Fluid Stream

. Bodies that Lose or Gain Mass Contents xxi

Planar Kinematics of a

Rigid Body

Chapter Objectives

. Planar Rigid-Body Motion

. Translation

. Rotation about a Fixed Axis - – Absolute Motion Analysis

. Relative-Motion Analysis: Velocity

. Instantaneous Center of Zero Velocity

. Relative-Motion Analysis:

Acceleration - – Relative-Motion Analysis using Rotating

Axes

Planar Kinetics of a Rigid

Body: Force and

Acceleration

Chapter Objectives

. Mass Moment of Inertia

. Planar Kinetic Equations of Motion

. Equations of Motion: Translation

. Equations of Motion: Rotation About a

Fixed Axis

. Equations of Motion: General Plane

Motion XXII Contents

Planar Kinetics of a

Rigid Body: Work and

Energy

Chapter Objectives

. Kinetic Energy

. The Work of a Force

. The Work of a Couple Moment

. Principle of Work and Energy

. Conservation of Energy

Planar Kinetics of a

Rigid Body: Impulse and

Momentum

Chapter Objectives

. Linear and Angular Momentum

. Principle of Impulse and Momentum

. Conservation of Momentum - . Eccentric Impact Contents xxiii

Three-Dimensional

Kinematics of a

Rigid Body

Chapter Objectives

Rotation About a Fixed Point - * The Time Derivative of a Vector Measured

from a Fixed or Translating-Rotating

System

General Motion - * Relative-Motion Analysis Using Translating

and Rotating Axes

Three-Dimensional

Kinetics of a Rigid

Body

Chapter Objectives - . Moments and Products of Inertia
- Angular Momentum
- Kinetic Energy
- * Equations of Motion
- * Gyroscopic Motion
- Torque-Free Motion XXIV Contents

Vibrations

Chapter Objectives

. Undamped Free Vibration - . Energy Methods
- . Undamped Forced Vibration
- . Viscous Damped Free Vibration
- . Viscous Damped Forced Vibration
- . Electrical Circuit Analogs

Appendix

A. Mathematical Expressions

B. Vector Analysis

C. The Chain Rule

Fundamental Problems

Solutions and

Answers

Review Problem

Answers

Answers to Selected

Problems

Index Index

A

Acceleration, dynamics and,

Active force,

Angles, –

Cartesian force vectors, –

coordinate direction, –

dot product used for,

dry friction and,

formed between intersecting lines,

horizontal ( ),

impending motion and,

kinetic friction ( *), –

lead,

mathematical review of, –

projection, parallel and perpendicular,

Pythagorean s theorem and,

resultant forces from,

screws,

static friction (^),

vectors and, –

vertical ( ,

Applied force (P), –

Area (A),

, –

axial symmetry and rotation,

centroid ( of an,

centroidal axis of, –

composite bodies (shapes), –

inclined axis, about, –

integration for, –

Mohr’s circle for, —

moments of inertia ( ) for,

Pappus and Guldinus, theorems of,

parallel-axis theorem for,

plane, volume generated revolution of,

polar moment of inertia, –

principal moments of inertia,

procedures for analysis of,

product of inertia for,

radius of gyration of,

surface of revolution,

transformation equations for,

volume of revolution,

Associative law,

Axes,

, –

area moments of inertia for,

centroidal axis of,

composite bodies, –

distributed load reduction,

inclined, area about, –

line of action for,

mass moments of inertia for,

Mohr’s circle for, –

moment of a force about specified,

moments of inertia (/),

, —

parallel-axis theorem for,

principal,

procedures for analysis o£ ,

product of inertia and,

radius of gyration for,

resultant forces and,

right-hand rule for, –

scalar analysis,

transformation equations for,

vector analysis,

Axial loads, friction analysis of, –

Axial revolution,

Axial symmetry, –

axial revolution and, — ,

centroid ( and,

composite bodies,

Pappus and Guldinus. theorems of,

rotation and,

surface area and,

volume and,

Axis of symmetry,

area (A) of, –

centroid ( and,

parallel-axis theorem for,

principal axes,

product of inertia,

B

Ball and socket connections,

Base units,

Beams, –

bending moments (M) and,

cantilevered,

centroid ( ,

couple moment (M) and,

distributed loads and,

force equilibrium, –

free-body diagrams,

internal forces, –

internal loads of, –

method of sections for,

moments,

normal force (N) and,

procedures for analysis of,

resultant loadings,

shear and moment diagrams, –

shear force (V) and,

sign convention for, Index

Beams (Conr/Hne^)

simply supported,

torsional (twisting) moment,

Bearings,

axial loads, –

collar, — ,

free-body diagrams, –

frictional analysis of. — ,

journal,

lateral loads, —

pivot, — ,

rigid-body support reactions, –

thrust,

Belts (flat), frictional analysis of,

Bending moment diagrams, – . See also Shear and

moment diagrams

Bending moments (M), –

distributed loads and,

internal forces and,

method of sections for, –

shear (V) and,

shear and moment diagrams, –

Body at rest (zero),

By inspection, determination of forces, –

C

Cables,

concentrated loads,

connections,

continuous,

distributed loads,

equilibrium of,

flexibility of,

free-body diagram for,

inextensible,

internal forces of,

sagging,

support reactions,

weight of as force,

Calculations, engineering importance of, –

Cantilevered beam,

Cartesian coordinate system, — ,

,

addition of vectors,

concurrent force resultants, — ,

coordinate direction angles, — , –

coplanar force resultants, –

cross product for, –

direction and, – . ,

dot product in,

force vector directed across a line, –

horizontal angles ( ),

magnitude of, — ,

moment of a force, calculations by,

position vectors (r),

rectangular components , — ,

right-hand rule,

sign convention for,

three-dimensional systems, —

two-dimensional systems, –

unit vectors, — ,

vector formulation,

vector representation, — , –

vertical angles (^),

Cartesian vector notation,

Center of gravity (G), –

center of mass (Cm) and,

centroid (C) as, –

composite bodies, — ,

constant density and,

coplanar forces,

free-body diagrams of,

location of, — ,

New ton s law of gravitational attraction and,

procedure for analysis of,

rigid-body equilibrium and,

specific weight and.

weight (W) and, — , .

Center of mass (Cm),

Center of pressure (P),

Centroid (C), –

area in r-y plane, — ,

axis of symmetry, — ,

axial symmetry, –

beam cross-section location,

center of gravity (G) as, –

center of mass (Cm) of a body,

composite bodies,

composite shapes,

coplanar forces,

distributed loads and,

distributed loads,

flat surfaces.

fluid pressure and. — ,

free-body diagrams for,

integration for determination of, — ,

line in x-y plane, — , — ,

line of action for, .

location of, . — ,

mass of a body (Cm),

method of sections and,

Pappus and Guldinus. theorems of. — ,

plates, —

procedure for analysis of, . Index

Pythagorean^ theorem for,

resultant forces and,

rigid-body equilibrium and,

rotation of an axis,

surface area and,

volume, of a,

Centroidal axis,

Coefficient of kinetic friction (/j*), —

Coefficient of rolling resistance, –

Coefficient of static friction (pj, –

Collar bearings, frictional analysis o£ ,

Collinear couple moment,

Collinear vectors,

Commutative law,

Component vectors of a force,

Composite bodies, M ,

area (A) of,

axial symmetry and,

center of gravity (G),

centroid (C) o£ ,

constant density and,

mass moments of inertia,

moments of inertia ( ),

procedure for analysis of,

theorem of Pappus and Guldinus for parts of,

specific weight and,

weight (W) and,

Compressive forces (C), –

method of joints and, –

method of sections and, –

truss members, –

Concentrated force,

Concentrated loads, –

cables subjected to,

distributed loads, –

sagging from,

shear and moment discontinuities from,

Concurrent forces,

,

addition of vectors, –

Cartesian coordinate system for, –

constraints and,

equilibrium of,

equivalent systems of, –

free-body diagrams,

force and couple systems, simplification of, –

lines of action for,

procedure for analysis of,

resultant couple moment,

statical determinacy and,

three-dimensional systems, –

three-force members, –

two-dimensional coplanar resultants,

Connections, free-body diagrams of, – . See also Joints;

Support reactions

Conservative forces, –

friction as nonconservative,

spring force,

virtual work (G) and, –

weight,

Constant density, center of gravity (G) and,

Constraints,

improper,

procedure of analysis of,

redundant,

statical determinacy and,

support reactions and, –

rigid-body equilibrium and,

Continuous cables,

Conversion of units,

Coordinate direction angles, — , –

Coordinates, . See also

Cartesian coordinate system

Cartesian, –

frictionless systems,

position, — ,

potential energy and,

right-hand rule for,

vector representation, –

virtual work for rigid-body connections,

x, y, z positions, –

Coplanar distributed loads, –

Coplanar forces,

, –

addition of systems of,

Cartesian vector notation,

center of gravity,

centroid (geometric center),

couple moments of, –

direct solution for unknowns,

direction of,

distributed load reduction, –

equations of equilibrium,

equilibrium of, –

equivalent systems of, –

free-body diagrams,

idealized models of, –

internal forces and,

lines of action, –

magnitude of,

particles subjected to,

procedure for analysis of,

rectangular components, Index

Coplanar forces

resultant couple moment

resultants, — , –

rigid bodies, –

scalar notation,

support reactions,

system components, –

systems, simplification of, –

two- and three-force members, —

vectors for,

weight and,

Cosine functions,

Cosine law,

Cosines, direction of, –

Coulomb friction, . See also Dry friction

Couple,

Couple moments (Mo),

, –

collinear,

concurrent force system simplification,

coplanar force system simplification,

distributed loading,

equivalent couples,

equivalent systems, –

force systems and, –

free vectors,

internal forces and,

parallel force system simplification,

procedure for analysis of,

resultants, –

right-hand rule for,

rigid bodies, equilibrium of, –

rotation of. , –

scalar formulation of,

shear and moment diagrams,

shear load (V) relationships,

support reactions and.

systems, simplification of, –

three-dimensional systems,

translation of,

vector formulation of, –

virtual work of,

w ork of,

wrench, reduction of forces to,

Cross product, –

Cartesian vector formulation, –

direction for,

laws of operation,

magnitude for,

right-hand rule for, –

vector multiplication using, –

Curved plates, fluid pressure and,

Cylinders, rolling resistance of, –

D

Deformation, rolling resistance and,

Derivatives,

Derived units,

Dimensional homogeneity,

Direct solution for unknowns,

Direction,

,

axis, moment of a force about, –

Cartesian coordinate vectors,

Cartesian vector notation,

coordinate direction angles,

coplanar force systems,

cross product and,

dot product applications, –

equilibrium and,

force vector along a line,

free-body diagrams,

frictional forces,

horizontal angle ,

impending motion and,

line of action, –

moment of a couple,

moment of a force (Mo),

position vectors,

right-hand rule for,

screws,impending motion of,

three-dimensional systems, –

translation,

vector sense of,

vertical angle

Direction cosines, –

Disks, — ,

frictional analysis of, — ,

mass moments of inertia,

Displacement ( ),

frictionless systems,

potential energy and,

principle of virtual work and,

procedure for analysis of,

rigid bodies, connected systems of, –

virtual work ([/) and,

virtual work equations for,

Distributed loads,

,

axis (single) loading,

beams subjected to, –

bending moment (M) relationships, Index

cables subjected to,

center of pressure (P),

centroid (C) of,

concentrated loads and, –

coplanar,

couple moment (Af#) relationships,

fluid pressure from,

force equilibrium, –

force system resultants,

incompressible fluids,

internal forces, –

linearly,

line of action of,

loading curve for,

magnitude and,

reduction of forces,

resultant forces of,

shear and moment diagrams, –

shear force (V) relationships,

uniform,

Distributive law,

Dot notation,

Dot product,

angles between intersecting lines,

applications of, —

Cartesian vector formulation,

laws of operation,

moment about a specified axis,

projections, parallel and perpendicular,

unit vectors and,

vector angles and direction from,

Dry friction, —

angles ( ) of, –

applied force (P) and, –

bearings, analysis of, — ,

belts (flat), analysis of, — ,

collar and pivot bearings, analysis of,

characteristics of,

coefficients of (p),

direction of force,

disks, analysis of,

equations for friction versus equilibrium, –

equilibrium and,

frictional force,

impending motion, –

journal bearings,analysis of,

kinetic force (F^),

motion and, —

problems involving, –

procedure for analysis of,

rolling resistance and,

screws, forces on,

sliding and,

slipping and,

static force (Fs),

theory of,

tipping effect, balance of,

wedges and,

Dynamics, study of, –

E

Elastic potential energy(VJ,

Engineering notation,

Equations of equilibrium,

, –

alternative sets for, –

body at rest (zero),

coplanar force systems, –

direct solution,

direction and,

frictional equations and, –

magnitude and,

particles, –

procedure for analysis using,

rigid bodies, –

scalar form, –

three-dimensional force systems,

two- and three-force members, –

vector form,

Equilibrium,

,

concurrent forces,

conditions for,

constraints, –

coplanar force systems, –

direction and,

distributed load relationships, –

free-body diagrams, –

friction and,

frictionless systems,

idealized models for, –

impending motion and,

improper constraints and,

neutral,

one (single) degree-of-freedom system, –

particles, –

potential-energy (V) criterion for,

procedures for analysis of,

redundant constraints and,

rigid bodies, –

shear and moment diagrams, –

stability of systems,

stable,

statical determinacy and, Index

Equilibrium (Conzmuei/)

statics and,

support reactions, –

three-dimensional force systems,

tipping effect, balance of,

two- and three-force members, –

two-dimensional force systems,

unstable,

virtual work (t ) and,

zero condition,

Equivalent couples,

Equivalent systems, –

concurrent force systems, –

coplanar force systems, –

external effects of,

force and couple moment simplification, –

lines of action of, –

parallel force systems, –

principle of transmissibility for,

procedures for analysis,

system of force and couple moments,

three-dimensional systems, –

wrench, reduction to,

Exponential notation,

External effects for equivalent systems,

External forces,

F

Fixed supports,

Flat belts, frictional analysis of,

Flat plates,

constant width,

distributed loads on,

fluid pressure and,

variable width,

Floor beams, truss analysis and,

Fluid pressure,

acceleration due to gravity (g),

center of pressure (P),

centroid (C),

curved plate of constant width,

flat plate of constant width,

flat plate of variable width,

incompressible fluids,

line of action,

Pascal’s law,

plates,

resultant forces and,

Force, –

,

, –

active,

addition of vectors, (>

applied (P), –

axis, about a specified,

basic quantity of mechanics,

beams, –

bending moments (M) and,

by inspection, –

cables,

Cartesian vector notation for,

components of,

compressive (C), –

concentrated, –

concurrent,

conservative, –

coplanar,

couple moments and,

cross product, –

directed along a line, –

displacements from, –

distributed loads,

dot product,

equilibrium and, –

equivalent systems, reduction to, –

external,

fluid pressure,

frames, –

free-body diagrams,

friction as,

frictional,

gravitational,?

idealized models for, –

internal, –

kinetic frictional (F^),

line of action,

,

machines, –

mechanics of,

method of joints and, –

method of sections for,

moment (M) of,

,

motion and, –

multiforce members,

Newton s laws, –

nonconservative,

normal (N), –

parallel systems, –

parallelogram law for, Index

particles subjected to, –

position vectors and,

principle of moments,

principle of transmissibility,

procedures for analysis of,

pulleys,

reactive,

rectangular components, –

resultant,

,

rigid bodies, equilibrium of, –

scalar notation for,

scalar formulation,

shear (V),

simplification of systems,

smooth surface contact,

spring (Fj),

springs,

static frictional (Fs),

structural analysis and, –

structural members,

systems of, –

tensile ( ), –

three-dimensional systems,

,

trusses, –

two- and three-force members, –

unbalanced,

units of, –

unknown, –

virtual work (U) and, –

weight,

work (W) of, –

wrench, reduction to,

vector formulation,

,

Frames,

free-body diagrams for,

multiforce members of,

procedure for analysis of,

structural analysis of ,

Free-body diagrams,

,

, –

beams,

cables,

center of gravity,

centroid (geometric center),

concurrent forces, –

coplanar force systems, –

constraints,

direction and,

equilibrium and,

, –

external forces and, –

frames,

idealized models of, –

internal forces and,

machines,

method of sections using, –

particle equilibrium, –

procedures for analysis using,

pulleys,

rigid bodies, –

smooth surface contact,

springs,

statical determinacy and,

structural analysis using, –

support reactions, –

three-dimensional systems,

trusses, –

virtual work, –

weight and,

Free vector,

Friction (F),

angles ( ) of, –

applied force (P), –

axial loads and, –

bearings, analysis of,

belts (flat), forces on, — ,

characteristics o£ ,

coefficients of (p),

collar bearings, analysis of,

Coulomb,

disks, analysis of,

dry, —

equations for friction and equilibrium, –

equilibrium and,

impending motion, —

journal bearings, analysis of ,

kinetic force (F^),

lateral loads and, –

nonconservative force, as a,

point of contact,

pivot bearings, analysis of, —

procedure for analysis of,

rolling resistance and,

screws, forces of,

shaft rotation and,

sliding and,

slipping and,

static force (FJ, Index

Friction (F) (Continued)

virtual work (£ ) and.

wedges and, – .

Frictional circle.

Frictional force. ,

Frictionless systems.

G

Geometric center, . . See also Centroid (C)

Gravitational attraction, Newton s law of,

Gravitational potential energy (Vg),

Gravity, Center of gravity (G)

Gusset plate, –

H

Hinge connections. , . –

Hyperbolic functions.

I

Idealizations (models) for mechanics. . –

Impending motion. . , –

all points of contact,

angle of static friction for,

coefficient of static friction (ps) for,

downward, .

dry friction problems due to, –

equilibrium and frictional equations for, –

friction and, – . –

no apparent.

points of contact, . (>-

procedure for analysis of,

screws and,

slipping, verge of,

tipping and,

upward, – .

Inclined axes, moment of inertia for area about, –

Incompressible fluids,

Inertia, see Moments of inertia

Integrals,

Integration. , . , – . . —

area ( ),centroid of. . , –

center of mass (Cm),determination of using, .

centroid (C),determination of using, . ,

,

distributed loads. ,

fluid pressure distribution from. ,

line, centroid of, –

mass moments of inertia, determination of using. ,

moments of inertia, determination of using. ,

parallel-axis theorem. ,

procedure for analysis using,

resultant forces determined by,

volume (V), centroid of. ,

volume elements for,

Internal forces, . – . –

beams subjected to. , –

bending moments (M) and, – . ,

cables subjected to,

compressive (C),

concentrated loads, –

couple moment (Af#) and.

distributed loads, – . , –

force equilibrium. –

free-body diagrams, – . ,

method of sections and, – . ,

moments (Af) and, –

norma] force (N) and. – .

procedures for analysis of, .

resultant loadings, – .

rigid-body equilibrium and.

shear and moment diagrams, – . , –

shear force (V) and. – . , .

sign convention for,

structural members with, – .

tensile (T),

torsional (twisting) moment, .

weight. ,

International System (SI) of units. . –

J

Joints, – . See also Method of joints

equilibrium of. –

loadings at, –

pin connections. –

procedure for analysis of.

truss analysis and. – . –

unknown forces, –

zero-force members, –

Joules (J), unit of,

Journal bearings. , – .

free-body diagrams, –

frictional analysis of, – .

support reactions. –

K

Kinetic frictional force (Ffr), – .

L

Lateral loads, friction analysis of, –

Lead of a screw,

Lead angle.

Length. . , – . ,

basic quantity of mechanics.

centroid (C) of lines. – . ,

integration for. – . ,

procedure for analysis of. Index

Pythagorean theorem for,

units of, –

Line of action,

,

centroid (Q location from,

collinear vectors,

distributed loads,

fluid pressure and,

force and couple system simplification, –

force vector directed along,

moment force-vector formulation, –

moment of a force about an axis,

perpendicular to force resultants, –

principle of transmissibility,

resultant force,

vector representation of, –

Linear elastic behavior,

Linear load distribution,

Lines, centroid (C) of – . See also Length

integration for, –

procedure for analysis of,

Loading curve,

Loads,

, .

See also Distributed loads

axial, —

beams, –

cables,

concentrated, –

distributed, M

fluid pressure, –

friction (f) and, –

internal, –

lateral, –

linear distribution of,

moment (Af) relations with,

plates, — ,

resultant forces, –

reduction of distributed, –

shaft rotation and, —

shear (V),

single axis representation,

structural analysis and, –

three-dimensional,

truss joints, –

uniform,

units of,

weight,

M

Machines,

free-body diagrams for,

multiforce members of,

procedure for analysis of,

structural analysis of,

Magnitude,

,

Cartesian vectors, –

coplanar force systems,

constant,

couple moments,

cross product and,

distributed load reduction and,

equilibrium and,

force components,

free-body diagrams,

integration for,

moments and,

Pythagorean theorem for,

resultant forces,

right-hand rule for,

sine and cosine laws for,

vector force addition and, –

vector representation of,

units of,

Mass,

basic quantity of mechanics,

center of (Cm),

integration of,

units of, –

Mass moments of inertia,

axis systems,

composite bodies,

disk elements,

integration for,

parallel-axis theorem for,

procedure for analysis of,

Pythagorean theorem for,

radius of gyration for,

shell elements. ,

volume elements for integration,

Mathematical expressions, –

Mechanics,study of,

Members,

. See also Beams

compressive force (C), –

equilibrium of forces, –

frame analysis,

internal loads(forces) in,

joint connections, –

machine analysis,

method of sections for, –

multiforce,

pin connections, – Index

Members (Continned)

procedure for analysis of,

tensile force (T), –

three-force, –

truss analysis, –

two-force, –

unknown forces, –

zero-force, –

Method of joints, — ,

compressive forces, –

procedures for analysis using,

space truss analysis, –

structural analysis using,

tensile forces, –

truss analysis,

unknown forces, –

zero-force members for, –

Method of sections,

beam analysis using,

compressive forces (C), —

external forces and, –

internal forces and, –

free-body diagrams for, –

procedures for analysis using,

shear and moment diagrams from,

space truss analysis,

structural analysis using, –

tensile forces (T), –

truss analysis,

unknown member forces, –

Models (idealizations), –

Mohr’s circle, –

Moment arm (perpendicular distance),

Moment axis,

direction and,

force about a,

force-vector formulation and,

right-hand rule for, –

scalar analysis of,

vector analysis of, –

Moments (A/), . See also

Couple moments

bending (M),

concentrated load discontinuities,

couple (Af^),

cross product for, –

direction and,

distributed loads and, — ,

equivalent systems, reduction to, –

force, of, –

force-vector formulation, –

free vector,

internal forces and,

magnitude and,

normal force (N) and, –

parallel force systems, –

perpendicular to force resultants, –

principle of moments,

principle of transmissibility,

procedures for analysis of,

right-hand rule for, –

resultant forces and, –

scalar formulation of,

shear loads (V) and,

sign convention for,

system simplification of, –

torque,

torsional (twisting),

Varignon’s theorem, –

vector formulation of,

wrench, reduction of force and couple to,

Moments of inertia ( ), –

algebraic sum o£

area (A),

axis of symmetry,

axis systems, –

composite bodies, –

disk elements,

inclined axis,area about, –

integrals,

integration and, –

mass,

Mohr’s circle for, –

parallel-axis theorem for,

polar, –

principle,

procedures for analysis of,

product of inertia and. ,

radius of gyration for,

shell elements,

transformation equations for,

Motion, – . See

also Revolution; Shaft rotation

bearings,

belt drives,

coefficients of friction (p) and,

downward,

equilibrium and frictional equations for, –

friction and, –

impending, –

kinetic frictional force ( >),

Newton s laws of,

points of contact, –

procedure for analysis of,

rolling resistance and,

screws and, Index

self-locking mechanisms,

shaft rotation,

sliding,

slipping (impending),

static frictional force (Ff),

upward,

verge of sliding,

wedges,

Movement, virtual,

Multiforce members, . See also Frames; Machines

N

Neutral equilibrium, –

Newton, unit of,

Newton’s laws, –

dynamics and,

gravitational attraction,

motion,

Nonconservative force, friction as a,

Normal force (N), –

dry friction and, –

equilibrium and,

impending motion and, –

internal forces as,

method of sections for,

Numerical calculations, importance of, –

P

Pappus and Guldinus, theorems of,

axial revolution and symmetry,

centroid (C) and,

composite shapes,

surface area and,

volume and, — ,

Parallel-axis theorem,

area (A) and,

centroidal axis for,

composite parts,

mass moments of inertia determined by,

moments of inertia determined by,

product of inertia determined by,

Parallel force systems,

equilibrium of, –

improper constraints, –

reactive, –

three-force members,

simplification of, –

Parallelogram law,

Particles, –

coplanar force systems,

defined,

equations of equilibrium, –

equilibrium of, –

free-body diagrams, –

gravitational attraction,

idealized model of.

Newton s laws applied to, –

nonaccelerating reference of motion,

procedures for analysis of,

three-dimensional force systems,

two-dimensional force systems,

zero condition,

Pascal’s law,

Perpendicular distance (moment arm),

Pin connections, –

concurrent forces of, –

coplanar systems,

free-body diagrams of, –

three-dimensional systems, –

truss member analysis, –

Pivot bearings, frictional analysis of, —

Planar truss,

Plates,

flat of constant width,

distributed loads on,

centroid (C),

curved of constant width,

flat of constant width,

flat of variable width,

fluid pressure and,

linear distribution on,

resultant forces acting on, – .

Point of contact,

friction and,

impending motion (slipping), –

kinetic friction and, –

motion (sliding), –

rolling resistance and, –

static friction and,

Polar moments of inertia, –

Position coordinates,

Position vectors (r),

Cartesian vector form,

head-to-tail addition, –

x, y z coordinates,

Potential energy (V),

elastic (VJ,

equilibrium, criterion for,

equilibrium configurations, –

frictionless systems,

gravitational (Vp,

position coordinates for,

potential function equations,

procedure for analysis of,

single (one) degree-of-freedom systems, – Index

Potential energy (V) (Con/inueJ)

stability of systems and,

virtual work (V) and,

Pow er-series expansions,

Pressure, see Fluid pressure

Principal axes,

Mohr’s circle for, –

principal moment of inertia and, –

procedure for analysis of,

product of inertia for,

Principle moments of inertia,

Mohr’s circle for, –

principal axes,

procedure for analysis of,

transformation equations for,

Principle of moments,

Principle of transmissibility,

Principle of virtual w ork,

Product of inertia,

axis of symmetry for, –

centroid for,

Mohr’s circle and, –

parallel-axis theorem for,

procedure for analysis of,

principal axes and,

Procedure for analysis, –

Projections, parallel and perpendicular,

Pulleys, free-body diagram of. ,

Purlins,

Pythagorean theorem,

Q

Quadratic formula,

R

Radius of gyration,

Reactive force, –

Rectangular components, –

coplanar force systems, –

force vectors of, –

resultant force,

Resultant forces,

,

axis, moment of force about,

beams, –

Cartesian vector components, ^

Cartesian vector notation for,

centroid (Q and,

concurrent forces, –

coplanar forces, –

couple moments,

cross product for, –

direction of,

distributed loads,

fluid pressure and,

force components and,

force system, –

integration for,

internal forces,

lines of action,

magnitude of,

method of sections for, –

moments of a force, –

parallel force systems, –

parallelogram law for,

perpendicular to moments, –

plates,

principle of moments,

procedure for analysis of,

reduction of distributed loads,

scalar formulation of,

scalar notation for,

system reduction for,

vector addition for, –

vector formulation of, –

vector subtraction for,

wrench, reduction to,

Revolution,

axial symmetry and, –

centroid (C) and,

composite shapes,

Pappus and Guldinus, theorems of,

plane area,

surface area,

volume from, ^ ,

Right-hand rule,

axis, moment of a force about, –

cross product direction, –

force-vector formulation,

moment of a couple,

moment of a force, –

three-dimensional coordinate systems,

Rigid bodies,

center of gravity,

centroid (geometric center),

conditions for, –

connected systems of,

constraints of, –

coplanar force systems, –

defined,

displacement ( ) and,

equations of equilibrium for, –

equilibrium of, –

external forces and,

force and couple systems acting on, –

free-body diagrams, – Index

frictionless systems,

idealized models of, –

internal forces and,

improper constraints for,

mechanics,study of,

position coordinates for,

potential energy and, –

procedures for analysis of,

redundant constraints for,

statical detcnninacy and,

support reactions, –

three-dimensional systems,

two- and three-force members, –

uniform,

virtual work (V) for,

weight and,

Rocker connections,

Roller connections,

Rolling resistance, frictional forces and,

Roof truss,

Rotation, – .

Revolution; Shaft rotation

Rounding off numbers.

S

Scalar notation,

Scalar product,

Scalar triple product,

Scalars,

,

axis, moment of force about,

couple moments, formulation by,

division of vectors by,

dot product and,

equations of equilibrium, –

magnitude of,

moment of a force, formulation by,

multiplication of vectors by. .

negative,

torque,

vectors and,

work of a couple moment,

Screws,frictional forces on,

Self-locking mechanisms,

Sense of direction,

Shaft rotation, ^ ,

axial loads, –

collar and pivot bearings,

disks,

frictional analysis of,

frictional circle,

journal bearings,

lateral loads, –

Shear and moment diagrams, –

beam analysis using,

couple moment (Mo) and,

discontinuities in,

distributed load relations and,

internal forces and, –

method of sections for,

moment (M) relations in, –

procedure for analysis of,

shear force (V) relations in, –

Shear force (V), –

beams,

bending moments (M) and,

concentrated load discontinuities,

couple moment (Mo) and,

distributed load relations,

internal forces, –

method of sections for, –

shear and moment diagrams, –

Shell elements, mass moments of inertia,

Significant figures,

Simple trusses,

Simply supported beam,

Sine functions,

Sine law,

Single degree-of-freedom systems, –

Sliding, –

friction and, –

kinetic frictional force (F*),

motion of, –

problems involving, –

verge of,

Sliding vector,

Slipping,

friction and,

impending motion of,

points of contact, –

problems involving, –

static frictional force (FJ,

Slug, unit of,

Smooth surface contact (support),

Solving problems, procedure for, –

Space trusses, structural analysis of,

Specific weight, center of gravity (G) and,

Spring constant (A),

Spring force (FJ, virtual work and,

Springs,free-body diagram of ,

Stable equilibrium,

Stability of a system. , . See also

Equilibrium

equilibrium configurations for,

free-body diagrams for,

improper constraints and, – Index

Stability of a system (Continua/)

neutral equilibrium,

one (single) degree-of-freedom system, –

potential energy and, –

procedure for analysis of,

reactive parallel forces, –

rigid-body equilibrium and,

stable equilibrium,

statical determinacy and,

unstable equilibrium,

virtual work and,

Static frictional force ( ^,

Statical determinacy,

equilibrium and, –

procedure for analysis of,

improper constraints and, –

indeterminacy,

redundant constraints and,

rigid-body equilibrium and,

stability and,

Statically indeterminate bodies,

Statics, –

basic quantities,

concentrated force,

equilibrium and,

force, –

gravitational attraction,

historical development of,

idealizations,

length, –

mass, –

mechanics study of, –

motion,

Newton’s laws, –

numerical calculations for, –

particles,

procedure for analysis of, –

rigid bodies,

study of, –

time,

units of measurement, –

weight,

Stiffness factor (£),

Stringers,

Structural analysis, –

beams, –

compressive forces (C), –

frames,

free-body diagrams, –

internal forces and, –

machines,

method of joints,

method of sections,

multiforce members,

procedures for analysis of,

shear and moment diagrams for, –

space trusses,

tensile forces (T), –

trusses, –

unknown forces, –

zero-force members, –

Structural members,see Members

Support reactions, –

coplanar force systems,

free-body diagrams, –

improper constraints, –

procedure for analysis of,

redundant constraints,

rigid-body equilibrium and, –

statical determinacy and,

three-dimensional force systems,

Surface area, centroid (C) and,

Symmetry, see Axial symmetry; Axis of symmetry

System simplification, –

concurrent force system, –

coplanar force systems, –

equivalent system, reduction to, –

lines of action and, –

parallel force systems, –

procedures for analysis,

reduction to a wrench,

system of force and couple moments,

three-dimensional systems, –

T

Tangent functions,

Tensile forces ( ), Ck , –

flat belts, –

method of joints and, –

method of sections and, –

truss members, –

Tetrahedron form,

Thread of a screw,

Three-dimensional systems, ^ ,

, .

See also Concurrent forces

addition of vectors,

Cartesian coordinate system for, –

Cartesian unit vectors, –

Cartesian vector representation, –

concurrent forces,

constraints for,

coordinate direction angles, –

direction angles for, – Index

dot product for,

equations of equilibrium,

equilibrium of, . ,

equivalent systems, –

force and couple moment system simplification. — ,

force vectors, – . ,

free-body diagrams,

magnitude of,

parallel system simplification, –

particles,

position vectors. ,

procedure for analysis of,

reactive parallel forces,

rectangular components, –

resultants, –

right-hand rule,

rigid bodies. ,

statical determinacy and. ,

support reactions for, – . ,

x, yf z position coordinates, . –

Three-force member equilibrium. –

Thrust bearing connections, .

Time,

basic quantity of mechanics,

units of,

Tipping effect, balance o£ ,

Torque, . See also Moments (Af)

Torsional (twisting) moment,

Transformation equations, moments of inertia ( ) and,

,

Translation,

Trapezoid, distributed loading of,

Triangle rule. .

Triangular truss,

Trigonometric identities.

Trusses. – . –

assumptions for design. ,

bridges. –

compressive force (C) and, – . –

floor beams.

gusset plate for, –

joints, –

method of joints,

method of sections. – . ,

planar.

procedures for analysis of,

purlins.

roof,

simple, – .

space trusses, – .

stringers,

structural analysis for, –

tensile force (T) and. , – . –

triangular,

zero-force members. –

Tw o-dimensional systems. , – .

See also Coplanar forces

Cartesian unit vectors. ,

coplanar force vectors, – .

free-body diagrams for, –

particle equilibrium. –

procedure for analysis of, . .

rigid-body equilibrium, –

scalar notation for,

Two-force member equilibrium, –

U

U.S. Customary (FPS) system of units,

Unbalanced force.

Uniform distributed load,

Uniform rigid bodies,

Unit vector (u). , – . , – . – See also

Cartesian coordinates

Cartesian vectors. ,

dot product and, — ,

three-dimensional, –

force components, –

force vectors. ,

Units of measurement, –

base,

conversion of,

derived, – .

International System (SI) of, –

prefixes.

rules for use,

U.S. Customary (FPS) system of,

Unknow n member forces, –

Unstable equilibrium. ,

V

Varignon’s theorem. —

Vectors, – . , . ,

addition of, –

addition of forces. , –

axis, moment of a force about. –

Cartesian coordinate system,

— ,

Cartesian notation for,

components of a force, – .

concurrent forces, ^ .

coplanar force systems, –

cross product method of multiplication, –

collinear, Index

Vectors (Continued)

couple moments, formulation by. –

direction and, – . – . ,

division by scalars,

dot product. — ,

equations of equilibrium,

force directed along a line, –

forces and. –

free. .

line of action, – . –

magnitude and, . , – . ,

moments of a force, formulation by, – . – .

multiplication by scalars, .

operations, –

parallelogram law for. ,

physical quantity requirements.

position (r),

principle of transmissibility,

procedure for analysis of,

projections, parallel and perpendicular,

rectangular components. , –

resultant couple moment. –

resultant of a force, – . ,

rigid-body equilibrium and, .

scalar notation for,

scalar triple product,

scalars and, . , .

sliding, .

subtraction of forces.

systems of coplanar forces. –

three-dimensional systems, – . , – .

triangle rule for,

two-dimensional systems, – .

unit, – . –

Virtual movement,

Virtual work (t/), –

conservative forces and, –

couple moment, work of, –

displacement ( ) and,

equations for,

equilibrium and,

force (F) and. ,

friction and,

frictionless systems,

movement as,

position coordinates for. , .

potential energy (V) and,

principle of, . ,

procedures for analysis using,

rigid-bodies, connected systems of, –

single (one) degree-of-freedom systems, . –

spring force (F,) and,

stability of a system. ,

weight (W) and,

work (W) of a force, –

Volume (V), . , – . –

axial rotation and symmetry. ,

centroid of (Q, . . , –

integration of. ,

Pappus and Guldinus. theorems of. — ,

plane area revolution and,

procedure for analysis of.

W

Wedges,

Weight (W), . ,

cables subjected to own. ,

center of gravity (G) and, . , –

composite body parts,

conservative force of,

gravitational attraction and,

internal force of,

rigid-body equilibrium and.

virtual work (t ) and,

Weightless link, support reactions of,

Work (W) of a force. – . See also Virtual work

couple moment, of a.

force, of a. –

virtual movement and,

Wrench, reduction of force and moment to. .

X

x, y, z position coordinates, — . , –

Z

Zero condition of equilibrium. , .

Zero-force members, method of joints and. ^- Index

A

n-s (acceleration-position) graphs.

a-t (acceleration-time) graphs. –

Absolute acceleration. ,

Absolute dependent motion analysis.

see Dependent motion analysis

Absolute motion analysis. – .

Absolute position,

Absolute velocity, .

Acceleration (a). , – . , .- . , – .

, – . – .

,

absolute, .

angular (a). . , –

average, .

centripetal.

circular motion and. , –

constant, . , .

continuous motion and. –

coordinating fixed and translating

reference frames, – .

Coriolis,

curvilinear motion and. ,

,

cylindrical components and,

‘

,

deceleration and,

displacement and.

equations of motion for,

, – . .

, – . ,

erratic motion and. –

fixed-axis rotation and. ,

, – .

fixed-point rotation and, –

force (F) and, – . –

general plane motion and. ,

, – .

graphs of variables,

gravitational (g),

hodographs and,

inertia and, –

instantaneous, .

kinematics of particles and,

. , – . ,

kinetics of a particle, –

magnitude of, — ,

mass (m) and, –

moment of inertia ( ) and, .

,

normal (h) components of,

, –

normal force (N) and, –

planar kinetics, equations of motion

for. – .

planar kinetics of rigid bodies,

planar kinematics of rigid bodies,

, – .

, –

procedure for analysis of, .

projectile motion and,

rectangular coordinates and,- .

rectilinear kinematics and. ,

,

relative.

relative-motion analysis and,

, – . .

resistance of body to.

rigid-body kinematics for. –

rotating axes, – . .

rotation and. , – .

rotational equations of motion,

,

sign convention for,

tangential (r) components of, — ,

, –

tangential force (tan) and,

three-dimensional rigid-body

motion. –

time and.

time derivative for. –

translating axes,

translation and, – . .

translation and rotation, –

translational equations of motion,

,

unbalanced force and. ,

velocity (v) and. ,

Amplitude of vibration,

Angular acceleration (ar), .

. –

cylindrical components,

fixed-axis rotation. ,

fixed-point rotation, –

time derivative for. –

Angular deceleration,

Angular displacement (t/ ),

Angular impulse and momentum,

principle of. –

Angular momentum (H). – .

,- . ,

angular impulse and. ,

arbitrary point A for.

center of mass (G) for,

conservation of. ,

- .

direction of.

eccentric impact and. ,

fixed-axis rotation and,

fixed point O for.

free-body diagrams for. , –

general plane motion and,

gyroscopic motion and,

kinetics of a particle. –

magnitude of,

moment of a force relations with.

moment of momentum,

principle axes of inertia.

principle of impulse and. – .

,

procedures for analysis of,

rectangular components of

momentum,

right-hand rule for,

rigid-body planar motion,- . , –

scalar formulation,

system of particles. . –

three-dimensional rigid bodies. - . , – .

torque-free motion and, –

translation and. ,

units of,

vector formulation,

Angular motion. , . , - . ,

fixed-axis rotation,

fixed-point rotation, –

gyroscopic, — ,

Angular position ( ),

Angular velocity (to). , . . - . –

cy lindrical components.

Euler angles for.

fixed-axis rotation, .

Index

Angular velocity (w) (Continued)

fixed-point rotation. –

gyroscopic motion and. –

nutation angle ( ), –

precession ( ), –

spin (^r), –

time derivative for. –

Apogee,

Areal velocity,

Average acceleration. ,

Average power.

Average speed,

Average velocity,

Axes, – . ,

, – . , –

, . ,

, –

acceleration (a) of,

angular motion and. ,

arbitrary, moment of inertia about.

circular motion and. , –

constant motion.

coordinating fixed and translating

reference frames. ,

, –

curvilinear motion. –

equations of motion for. ,

, –

Euler’s equations for, –

fixed, –

fixed, rotation about,

, . ,

fixed reference frame, –

impulse and momentum of,

inertia (/), principle axes of, –

kinematics of a particle. ,

,

kinematics of rigid bodies, .

, – .

- . , –

kinetic energy and, .

moments of inertia (I) about,

pinned-end members, – . —

planar (normal and tangential)

motion. –

planes of symmetry,

position coordinates for,

position vector (r) for.

procedure for analysis of,

relative-motion analysis of, – .

, – . ,

, –

rigid-body planar motion,

,

- . – . , .

,

rotating, – . , –

rotation about, . – . - . ,

rotational equations of motion for, - . , –

slipping. –

symmetrical spinning axes. –

three-dimensional particle motion.

three-dimensional rigid-body

motion, –

translating, . ,

translating frames of reference,

,

translation and rotation,

- . –

translational equations of motion

for, . ,

velocity (v),

Axis of rotation,

Axisymmetric characteristics,

B

Base point,

Binormal coordinates, . .

Body cone, –

C

Cartesian vector notation,

Center of curvature,

Center of mass (G), - . , –

angular momentum (H) and,

,

kinetic energy and,

moments of inertia and. ,

parallel-axis theorem and. –

rigid-body planar motion, –

rotational equations of motion and,

systems of particles and.

three-dimensional rigid bodies,- . , –

Center of percussion.

Central-force motion. ,

areal velocity,

circular orbit,

conservation of angular momentum.

directrix.

eccentricity (e), – .

elliptical orbit. –

equations of motion, –

escape velocity.

focus.

gravitational attraction (G) and,

Kepler’s laws,

kinetics of a particle, –

parabolic path,

path of motion. –

space mechanics and, –

trajectories,

velocity (v) and, –

Central impact, – . , –

coefficient of restitution (e),

conservation of momentum for. ,

deformation impulse.

kinetics of a particle,

principle of impulse and

momentum for.

procedure for analysis of,

restitution impulse.

Centripetal acceleration.

Centripetal force,

Centrode. –

Chain Rule, –

Circular motion. ,

,

acceleration (a), –

instantaneous center (IC) of zero

velocity. ,

planar rigid-body motion. — ,

, –

position and displacement from.

procedures for analysis of. ,

relative-motion analysis of,

, –

*

relative velocity and,

right-hand rule for.

rolling without slipping,

rotation about a fixed axis, –

velocity (v), – . , Index

Circular orbit.

Circular path of a point,

Coefficient of restitution, – .

, – .

Coefficient of viscous damping.

Complimentary solution, vibration,

Composite bodies, moment of inertia

for,

Conservation of energy,

, . ,

conservative forces and, – .

, – . –

displacement and. .

elastic potential energy. ,

gravitational potential energy, .

kinetic energy and. –

kinetics of a particle, – .

natural frequency (wn) from.

,

nonconservative forces and,

potential energy (V) and,

, — .

procedures for analysis using,

.

rigid-bodv planar motion. ,

system of connected bodies,

systems of particles,

time derivative for, – .

vibration and. ,

weight ( ¥), displacement of,

work (W) and, .

— ,

Conservation of mass,

Conservation of momentum,

, – . , – .

,

angular, . ,

eccentric impact and. –

impact and, . ,

impulsive forces and. –

kinetics of a panicle,

,

linear, – . ,

,

nonimpulsive forces and. –

procedures for analysis of,

,

rigid-body planar motion,

,

systems of particles,

Conservative force. ,

— , –

conservation of energy,

. , . –

elastic potential energy, .

friction force compared to. ,

gravitational potential energy,

. ,

potential energy (V) and,

. ,

potential function for. –

procedure for analysis of,

spring force as, – . ,

vibration and, –

weight (W), displacement of.

,

work (£ ) and. – . ,

,

Constant acceleration, .

Constant force, work of, . ,

.

Constant velocity,

Continuous motion,

acceleration (a), –

displacement (A),

kinematics of particles,

position ( ),

procedure for analysis of,

rectilinear kinematics of,

time (f),functions of,

velocity (v), –

Control volume, –

fluid flow. –

fluid streams, –

kinematics of a particle. –

mass flow. ,

mass gain and loss (propulsion),

procedure for analysis of,

steady flow. –

volumetric flow (discharge),

Coordinates,

, – . ,

, – . . , –

, . ,

. , –

acceleration (a) and. , – .

. , . – . ,- . , –

angular motion.

angular momentum (H) and,

binormal, . ,

centripetal force,

circular motion. –

continuous motion,

coordinating fixed and translating

reference frames,

curvilinear motion, — . ,

, –

cylindrical (r. ,z), – .

dependent motion analysis and,

,

directional angle ( ^), –

dot notation for.

equations of motion and. ,

,

fixed origin ( ),

fixed reference frame. , – .

, –

force (F) and, –

frictional forces (F) and,

inertial, –

kinematics of a particle, – .

, – . , – .

kinetic energy. –

kinetics of a particle. – .- . ,

normal (n), – . , – . .

normal forces (N) and, –

planar motion, —

polar, –

position ( ),

position-coordinate equations,

,

position vector (r). , . – .

procedures for analysis using, . ,

. ,

radial (r). –

rectangular (x,y, z). ,

, – .

relative-motion analysis and. – .

, .

rigid-bodv planar motion,- . , – Index

Coordinates (Continued)

rotating reference frame for.

rotation about a fixed axis,

rotational motion. –

symmetrical bodies, ^

tangential (f), . ,

. –

tangential forces (tan) and. –

three-dimensional motion. ,

,

translating axes and. ,

translating reference frame,

,

translating systems, – .

transverse ( ), –

velocity (v) and. , . ,

Coriolis acceleration,

Couple moment (A/), work (W) of a,

,

Critical damping coefficient.

Critically damped vibration systems,

Cross product. –

Curvilinear motion, – .

- . –

acceleration (a). ,

center of curvature (O’),

coordinates for. ,

cylindrical components,

cylindrical (r, . z) coordinates,

displacement (A),

fixed reference frames for. ,

, –

general, –

normal (n) axes. ,

kinematics of a particle. ,

, –

planar motion. –

polar coordinates, – .

position ( ), . ,

procedures for analysis of. ,

radial coordinate (r). –

radius of curvature (p),

rectangular (x,y, z) coordinates,

,

tangential (f) axes, — ,

time derivatives of, — .

three-dimensional motion.

transverse coordinate ( ), –

velocity (v). , .

Curvilinear translation,

,

Cycle, vibration frequency,

Cylindrical components. – . ,- .

acceleration (a) and. ,

curvilinear motion,

directional angle (^f). –

cylindrical (r. ,z) coordinates,

- .

equations of motion and, — ,

friction (F) force.

normal force (JV) and. –

polar coordinates for. ,

position vector (r) for,

procedures for analysis using,

radial coordinate (r), –

tangential force and. –

time derivatives of.

transverse coordinate ( ), –

velocity (v) and,

D

D’Alembert principle.

Damped vibrations,

critically damped systems,

motion of.

overdamped systems.

resonance from. .

underdampod systems.

viscous forced,

viscous free. ,

Damping factor.

Dashpot,

Deceleration, .

Deformation, — ,

central impact and, – .

coefficient of restitution (e),- . –

conservation of momentum and.

displacement and. –

eccentric impact and. –

elastic impact and.

friction force and,

impact and. , –

impulse.

kinetics of a particle,

localized.

maximum,

oblique impact and. ,

period of,

plastic impact and,

principles of work and energy and.

restitution phase,

rigid-body planar motion. –

separation of contact points.

sliding and,

systems of particles. –

Dependent motion analysis. – .

particle kinematics,

position coordinates for. ,

procedure for,

time derivatives for. – .

time-differential equations, – .

Derivative equations, –

Diagrams for impulse and momentum.

Direction, . , . ,

. – . ,

acceleration (a) and,

angular acceleration (a).

angular displacement (J ),

angular momentum,

constant,

force displacement and. –

instantaneous center (IC) of zero

velocity from.

relative-motion analysis. ,

right-hand rule for. . ,

rotation about a fixed axis, –

three-dimensional rigid bodies,

translation and rotation, .

velocity (v) and, . ,

,

Directional angle ( ^), –

Directrix.

Disk elements, moment of inertia of.

Displacement (A or J). , . ,

, – . , . ,

. . , . ,

,

acceleration (a) as a function of. Index

amplitude, –

angular (d ),

circular motion and,

conservation of energy and. ,

continuous motion and.

couple moment (A/) and,

curvilinear motion,

deformation from, –

erratic motion,

graphing determination of,

kinematics of a particle, .

kinetics of a particle, – .

periodic support,

phase angle (^),

position change as, .

principle of work and energy,

,

relative-motion analysis and.

resonance and,

right-hand rule for direction of. ,

rigid-body planar motion. , .

,

rotation about a fixed point, .

. –

simple harmonic motion,

sliding.

spring force and. , –

system of particles, –

three-dimensional rigid bodies.

translation and rotation causing,

vertical,

vibration and. ,

weight (W) and. , –

work of a force and,

,

work of a weight and.

Distance, . See also Displacement

Dot notation,

Dot product,

Drag force,

Dynamic equilibrium,

Dynamics, –

principles of. –

procedure for problem solving,

study of.

E

Eccentric impact, – .

Eccentricity (e),

Efficiency (e),

energy (£) and. – .

mechanical, –

power (P) and,

procedure for analysis of,

Elastic impact,

Elastic potential energy, . . ,

.See also Spring force

Electrical circuit analogs, vibrations

and,

Elliptical orbit, –

Energy (E), – . –

. , – .

conservative forces and,

. ,

conservation of,

, – .

efficiency (e) and. – .

elastic potential. , .

gravitational potential,

heat generation,

internal.

kinetic. ,

, – . – . .

,

kinetics of a particle, —

mechanical, – .

natural frequency (^) and,

,

potential (V), – .

power (P) and,

principle of w ork and, – .

, – . ,

procedures for analysis of. , .

. .

rigid-body planar motion and.

system of connected bodies,

systems of particles, — ,

three-dimensional rigid bodies,

,

time derivative for. ,

work (U) and. – . –

vibration and, – .

Equations of motion, – .

, – . ,

, – . , –

. , . ,

acceleration (a) and. ,

, – . – .

,

central-force motion. –

centripetal force,

cylindrical (r. , z) coordinates,- .

dynamic equilibrium and.

external force. , –

fixed-axis motion. –

fixed-axis rotation,

force (F) andJ . – . – . - . ,

free-body diagrams for. ,

, –

friction (F) force. ,

general plane motion, . — .

gravitational attraction (G),

- . –

inertial reference frame for. - . . — , –

instantaneous center (IC) of zero

velocity and,

internal force. , –

kinetic diagrams for,

kinetics of a particle. ,- . , – . .
- . –

linear impulse and momentum.

mass (m) and, . –

moment equation about

instantaneous center (IC),

moment equation about point O.

moments of inertia (/) and. ,

Newrtons second law,

normal (n) coordinates,

normal (N) force. ,

planar kinetics, — ,

principle of work and energy.

procedures for analysis using, –

. . . . ,

rectangular (r, y, z) coordinates.

, —

rigid-bodv planar motion. – .- . ,

rotational equations of motion. —

,

slipping and.

spring force. Index

Equations of motion (Continued)

symmetrical spinning axes, –

symmetry of reference frames for,

‘

systems of particles, –

tangential (f) coordinates,

tangential force,

three-dimensional rigid bodies,

,

trajectories, –

translational equations of motion,

,

Equilibrium,equations of motion and,

Equilibrium position, vibrations,

,

Erratic motion,

a-s (acceleration-position),

a-t (acceleration-time), –

integration of equations for,

particle rectilinear kinematics for,

,

s-r (position-time), –

v-s (velocity-position),

v-r (velocity-time), –

Escape velocity,

Euler angles,

Euler’s equations, –

Euler’s theorem,

External force,

External impulses, –

External work,

F

Finite rotation,

Fixed-axis motion,

equations of motion for,

Euler’s equations of motion for,

gyroscopic motion,

,

three-dimensional rigid bodies,

,

symmetrical spinning, –

Fixed-axis rotation,

,

acceleration (a) of,

,

angular acceleration (a),

angular displacement (^),

angular motion and,

angular position ( ),

angular velocity (oj),

circular motion, –

circular path of a point, –

displacement from,

equations of motion for,

,

force (F) of,

impulse and momentum for,

kinetic energy and,

kinetics,

moment equation about point ,

normal (n) coordinates, –

path of,

position and,

procedure for analysis of,

right-hand rule for,

rigid-bodv planar motion,

,

,

tangential (t) coordinates –

velocity (v) of,

Fixed origin (O),

Fixed-point motion,

angular momentum (H) for,

kinetic energy of,

three-dimensional rigid bodies,

,

Fixed-point rotation,

acceleration (fl) and,

angular acceleration (a) of, –

angular velocity components of,

, –

displacement from, –

Euler’s angles for,

Euler’s theorem for,

finite rotation,

fixed-axis and, –

infinitesimal rotation,

sphere as representation of,

three-dimensional rigid bodies,

, –

time derivatives for, –

velocity (v) and,

Fixed reference frame,

,

Fluid flow,

control volume for, –

fluid stream,

kinetics of a particle, –

mass flow, –

mass gain and loss (propulsion),

,

procedure for analysis of,

steady,

system of particles, –

volumetric flow (discharge),

Focus,

Force (F),

,

,

,

, – . See

also Central-force motion

acceleration (fl) and,

angular momentum relations with,

central-force motion and,

centripetal,

conservation of energy and,

, –

conservation of linear momentum

and, –

conservative, — ,

constant,

couple moment (Af) and,

damping, –

displacement (d) from,

— ,

elastic potential energy from,

energy and, –

equations of motion for, —

,

,

external,

fixed-axis rotation and,

free-body diagrams for,

, –

friction (F),

general plane motion and, —

gravitational attraction (G) as,

, – Index

impulsive, –

inertia force vector,

internal, –

kinetics of a particle,

,

, –

linear impulse and momentum of,

planar kinetics, equations of motion

for,

potential energy (V) and,

, –

principle of work and energy and,

procedure for analysis of,

mass (m) and. –

moments of a, –

moments of inertia ( ) and,

^ ,

Newton’s laws and,

nonconservative,

normal (N), –

normal coordinates for, –

periodic, –

planar motion and,

,

potential energy (V) and,

potential function for, –

propulsion (mass gain and loss),

,

resultant,

rigid-bodv kinetics,

,

rolling without slipping,

rotational equations of motion,

— ,

slipping (no work),

spring,

, –

straight-line path of,

system of particles,

, –

tangential, –

tangential coordinates for,

trajectories,

translational equations of motion,

,

unbalanced,

units of,

variable,

vector,

vibrations and,

, –

viscous damping, –

weight (W),

,

work (f/) of,

,

Forced vibrations,- . –

damped. ,

equilibrium position of,

forcing frequency (cu ) for,

magnification factor (MF) for,

,

motion of,

periodic force and, –

periodic support displacement of,

resonance from,

steady-state of, –

undamped,

viscous damped,

Free-body diagrams,

, –

angular momentum, –

equations of motion and,

inertial reference frames,

kinetics of particles using,

, –

linear impulse and momentum,

rigid-body planar motion, –

rotational motion, –

translational motion,

Free-flight trajectory,

Free vibrations,

motion of,

transient state of,

undamped,

viscous damped,

Frequency (/),

,

cycles of,

damped natural (wj),

energy conservation and, –

forcing (gjo),

natural (wn),

procedure for analysis of,

unit of,

vibration and. ,

,

Frequency ratio,

Friction force (F),

conservative forces compared to,

,

equations of motion for,

principle of work and energy for,

work of caused by sliding,

G

Gage pressure,

General plane motion,

,

,

, . See also Planar motion

absolute motion analysis for,

,

acceleration (a),

,

angular momentum and,

displacement (d) from,

equations of motion for,

,

force (F) and,

impulse and momentum for,

instantaneous center (IC) of zero

velocity,

kinetic energy and,

linear momentum and,

moment equation about the

instantaneous center (IC),

path of,

position (r) and,

procedure for analysis of,

,

relative-motion analysis for, –

, –

rigid-body kinematics,

, –

rigid-body kinetics, — ,

,

rolling without slipping,

rotating axes,

rotation and translation,

velocity (v),

, Index

General three-dimensional motion.

,

Graphs. – . . ,

constant and variable force

representation,

erratic motion represented by.- .

impulse represented by. ,

rectilinear kinematic solutions

using,

Gravitational acceleration (g),

Gravitational attraction (G). ,

central-force motion and, –

Newton’s law of. –

Gravitational potential energy,

,

Gyroscopic motion, – . ,

angular momentum (II) and.

angular motion of. ,

angular velocity components for,

equations of motion for. –

Euler angles for,

gyro,

gyroscopic effect,

nutation angle ( ), –

precession ( ),

spin ( ), –

symmetrical spinning axes, –

H

Heat, friction forces from sliding and.

Hertz (Hz), unit of,

Hodographs, particle acceleration

and,

Horizontal projectile motion, –

Horsepower (hp), unit of,

Hyperbolic functions.

Hyperbolic trajectory,

I

Impact, – .

central. ^, –

coefficient of restitution (e),

,

conservation of momentum,

, –

deformation and. , –

eccentric. ,

elastic,

energy loss from,

kinetics of a particle. ,

line of, . ,

oblique,

plane of contact. . ,

plastic (inelastic). .

principle of impulse and

momentum for,

procedures for analysis of,

restitution phase, – .

rigid-body planar motion, – .

separation points of contact (C),

Impulse, .

angular. ,

conservation of angular momentum

and.

conservation of linear momentum

and. ,

control volumes, –

diagrams,

equations of motion for, –

external. –

graphical representation of. ,

impact and. , – .

internal, –

kinetics, –

linear. , –

magnitude of,

mass flow, –

mass gain and loss (propulsion),

,

momentum and. , —

particles. –

principle of momentum and.- . — , . ,

, .

procedures for analysis of, .

,

restitution,

rigid-body planar motion, –

steady flowr and,

three-dimensional rigid bodies,

time (/), as functions of, –

Impulsive forces, –

Inertia ( ), – . , .

- . ,

acceleration (a) and, . . ,

angular acceleration (a) and,

angular momentum (H) and.

arbitrary axis, moment of about.

composite bodies,

equations of motion and. ,

integration of. — , –

mass center (G) and. , –

mass moments of. –

moment equation about the

instantaneous center (IC),

moment equation about point G,

moment of, – . ,

, – . ,

parallel-axis theorem. ,

parallel-plane theorem.

principle axes of, – .

principle moments of, .

procedure for analysis of,

products of,

radius of gyration,

resistance of body to acceleration,

rigid-body planar motion and,

, . ,

slipping and.

three-dimensional rigid-body

motion,

volume elements for integration of,

Inertia tensor. –

Inertial reference frames,

,

, –

angular momentum (H). –

equations of motion. – . .

, –

force vector,

kinetic energy, –

kinetics of a particle,

rigid-body planar motion. ,

rotational motion. , –

slab in. –

symmetry of. —

three-dimensional rigid-body

motion,

translational motion, . Index

Infinitesimal rotation.

Instantaneous acceleration,

Instantaneous axis of rotation.

,

Instantaneous center (IC),

,

centrode.

circular motion and,

general plane motion, – .

location of, –

moment equation about,

procedure for analysis of,

relative-position vector for, –

slipping and.

zero velocity, – . .

Instantaneous power,

Instantaneous velocity,

Integral equations. –

Integration of equations, – .- . –

erratic motion,

kinetic energy. –

moments of inertia. ,

products of inertia. –

three-dimensional rigid bodies. - . –

Internal energy,

Internal force, . ,

Interna] impulses, –

J

Joule (J), unit of,

K

Kepler’s laws,

Kinematics. , – .

See also Planar motion

absolute motion analysis,

continuous motion, –

coordinates for, – . – .

, —

curvilinear motion, – .

, – . –

cylindrical components. –

cylindrical (r, z) coordinates,

dependent motion analysis,

erratic motion,

fixed-axis rotation,

fixed-point rotation,

graphs for solution of,

instantaneous center (IC) of zero

velocity,

motion and,

normal («) axes. ,

particles and. –

planar, –

polar coordinates, –

position (r),

position coordinates. . ,

principle of,

procedures for analysis of. . ,

, . , . ,

.

projectile motion, – .

radial (r) coordinate, –

rectangular (x, y, z) coordinates,

,

rectilinear. , – . , –

relative-motion analysis,

, – . ,

,

rigid bodies, – . —

rotating axes, – . . ,

,

rotation and. ,

, – . –

sign conventions for, –

tangential ( r) axes. ,

three-dimensional motion. ,

time derivatives. , . ,

translating axes,

. , – .

translating-rotating systems.

translation and, – . ,

, – . –

transverse ( ) coordinate, –

Kinetic diagram, . . –

Kinetic energy, – .

. , – . ,

,

conservation of energy and,

, –

center of mass (G) for,

fixed-point O for.

general plane motion and, .

inertial coordinate system for,

integration for. , –

kinetics of particles, – . .- .

potential energy and, –

principle of work and energy.

, .

procedure for analysis of, . ,

rigid-body planar motion and. - . ,

rotation about a fixed axis and,

slab in inertial reference for,

system of bodies.

three-dimensional rigid-body

motion, – .

translation for. ,

Kinetic moments,

Kinetics, – . – .- . ,
- . See a/so Planar motion;

Space mechanics

acceleration (a) and. ,

angular momentum (II),

,- .

central-force motion. – .

conservation of energy,

conservation of momentum, - . , – .

conservative forces and. – .

control volumes, –

cylindrical (r. ,z) coordinates,

- .

eccentric impact, – .

efficiency (e) and,

energy (£) and,

equations of motion, . ,- . , — , –

, – .

fixed-axis rotation, .

, . .

fluid flow,

force (F) and, – . ,

, – . –

free-body diagrams for. ,

, –

gyroscopic motion, - . Index

Kinetics (Cwi/mwerf)

impact,

impulse,

inertia ( , . ,

,

inertial reference frame for

,

linear momentum,

, . –

mass (m), –

mass flow, –

mass gain and loss (propulsion),

- .

mass moments of inertia. ,

momentum. – . ,

Newton s laws and, – .

normal (n) coordinates, – .

particles, – . – . –

planar motion. ^ , – .

potential energy and, – .

power (P), – .

principle of,

principle of impulse and

momentum,

,

principle of work and energy,

, – . ,

procedures for analysis of. ,

, . , . ,

, . . ,

,

propulsion (mass gain and loss),- .

rectangular (x.y.z) coordinates, - . ,

rigid-bodies. . , – .

rotation and,

rotational equations of motion,

, – . ,

spring force,

steady flow. ,

systems of particles. – . –

tangential (f) coordinates. ,

three-dimensional rigid bodies,

torque-free motion, – .

trajectories,

translation and. ,

translational equations of motion,

,

work (£ ) and,

,

L

Line of action,

Line of impact. ,

Linear impulse and momentum. –

,

, –

conservation of momentum.- . ,

diagrams for,

equations of motion for, –

fixed-axis rotation and,

force (F) and, –

impulsive forces and, –

general plane motion and,

kinetics of a particle. , - .

principle of. ,

procedures for analysis of, .

rigid-body planar motion,

- . –

systems of particles, – .

‘ - .

time (/), as functions of, –

translation and. ,

vectors,

M

Magnification factor (MF),

Magnitude, . ,

- . . , .

, . ,

acceleration (a), . , . .

angular acceleration (a),

angular displacement (d^) and.

angular velocity (<t?) and,

angular momentum (II).

average speed.

constant. ,

couple moment (A/), work of and,

,

curvilinear motion and,

, – .

distance as,

fixed-axis rotation and.

graphical representation of,

instantaneous center (IC) of zero

velocity from.

kinematics of a particle,

, – . ,

linear impulse,

planar kinematics,

position vector (r) and.

rectilinear kinematics and, –

relative-motion analysis and, .

,

rigid-body planar motion. ,

rotating axes, changes in motion

from. ,

rotation,changes in motion from.

speed as. . , .

time rate of change of,

velocity (v), . ,

Mass (m), – . – . – .

, – . – . See also

Center of mass (G)

acceleration (a) and,

conservation of,

control volumes for, –

equations of motion and. ,

fluid flow, –

gravitational attraction and.

linear momentum and, –

loss and gain of (propulsion).- .

moments (Af) of inertia (Z). —

Newton’s laws and, –

particle. –

principle of impulse and

momentum. –

propulsion (gain and loss of). - .

rigid-body planar motion. ,

steady flow of fluid systems and,

,

system of particles and, – .

weight and, Index

Mass flow, –

Mathematical expressions, –

Maximum deformation,

Mechanical efficiency, –

Mechanical energy, . See

also Conservation of energy

Mechanics, study of,

Moment arm,

Moment of a force, –

angular momentum and, –

external force,

internal force,

kinetics of a particle, –

resultant force and, –

systems of particles,

Moment of inertia, – L ,

,

acceleration (a) and,

,

arbitrary axis, about,

body resistance to acceleration,

composite bodies,

disk elements,

equation about the instantaneous

center (IC),

equation about point ,

equations of motion and,

fixed-axis rotation,

force (F) and,

general plane motion,

inertia tensor for, –

integration of, — ,

mass, —

mass center (G), –

parallel-axis theorem for,

,

parallel-plane theorem for,

principal,

procedure for analysis of,

products of inertia and, –

radius of gyration for,

rigid-body planar motion,

,

rotational equation of motion and,

shell elements,

single integration of,

slipping and,

three-dimensional rigid-body

motion,

volume elements for integration of,

Moment of momentum, . See also

Angular momentum

Moments, work of a couple,

Momentum, — ,

,

angular (H),

,

,

conservation of,

,

control volumes, –

diagrams for,

equations of motion for, –

fixed-axes rotation and,

general plane motion and,

impact and,

,

impulse and, –

kinetics, –

linear (L),

, –

mass flow, –

mass gain and loss (propulsion),

,

moments of force and, –

particle, –

principle axes of inertia and,

principle of impulse and,

,

,

procedures for analysis of,

,

rectangular components for,

rigid-body planar motion, –

steady flow and,

systems of particles,

,

three-dimensional rigid bodies,

,

time (f),as functions of, –

translation and. ,

vector form,

N

Natural frequency ,

,

damped (<j j),

energy conservation and, –

procedures for analysis of,

undamped free vibration, .

,

underdamped systems,

vibration and,

,

Newton’s laws,

body mass and weight from,

equation of motion,

gravitational attraction, –

inertia and, –

kinetics of particles and,

second law of motion,

unbalanced force and, –

Newtonian inertial reference frame,

Nonconservative force,

Nonimpulsive forces, –

Nonrigid bodies, principle of work and

energy for,

Normal (n) coordinates,

, –

acceleration (a) and,

, –

circular motion components,

curvilinear motion components,

equations of motion and,

kinematics, –

kinetics,

particles, –

planar motion and, –

procedure for analysis of,

rigid-bodies, –

rotation about a fixed axis, –

three-dimensional motion,

velocity (v) and,

Normal (N) force, –

Nutation angle (fl), –

O

Oblique impact,

Orbit,central-force motion of, –

See also Trajectories

Orbital revolution,

Osculating plane,

Overdamped vibration systems, Index

P

Parabolic path.

Parallel-axis theorem. ,

Parallel-plane theorem,

Particles. – . ,

acceleration (a), – . , – .

, –

angular impulse of, –

angular momentum (II) of, – .

central-force motion of,

conservation of angular momentum.

,

conservation of energy,

conservation of linear momentum.

,

conservative forces and,

continuous motion of, –

control volume, –

coordinates for. ,

- . ,

,

curvilinear motion of – . , - . –

deformation of. — , –

dependent motion analysis, – .

displacement (A), –

efficiency (e) and. – .

energy (E) and. –

equations of motion, – .

, — . ,

erratic motion of. ,

force (F) and. ,

- . –

free-body diagrams. ,

gravitational attraction (G).

, –

hodographs.

impact, –

impulse, –

impulsive forces. –

inertial reference frame, – .

kinematics of, –

kinetic diagrams,

kinetic energy of,

kinetics of, –

mass (m), –

mass flow, –

mass gain and loss (propulsion),

,

momentum, –

Newton s second law of motion,- .

normal coordinates (n) for, –

planar motion of. –

position ( ),

position vector (r). , .

position-coordinate equations. –

potential energy of,

power (P) and. – .

principle of work and energy for. - . –

principles of impulse and

momentum, - .

procedures for analysis of, .

, . ,

, . . , .

projectile motion of. — ,

rectilinear kinematics of. ,

,

relative motion analysis. ,

resultant force on, –

speed (magnitude), . ,

,

spring force. — , – .

straight-line path of,

system of , – . .

, – . . ,

tangential coordinates (f) for,

three-dimensional motion of,

time (/).functions of

time derivatives, – . , – .

trajectories,

translating axes, two particles on,

,

velocity (v), -^ , . ,

work (£ ) and, –

Particular solution, vibration, –

Path of motion. –

Perigee.

Period of deformation,

Period of time, vibration,

Periodic force. –

Periodic support displacement,

Phase angle (),

Pinned-end members, – .

,

acceleration (a) and, –

coordinating fixed and translating

reference frames,

relative-motion analysis of,

,

velocity (v) and, –

Planar motion. ,

, – . See

also General plane motion

absolute motion analysis,

acceleration (a) and,

, – . ,

, –

angular momentum,

, –

angular motion and,

conservation of energy. ,

conservation of momentum,

,

couple moment (Af) in. ,

curvilinear. –

displacement (d),

eccentric impact. ,

energy (E) and, –

equations of motion for,

, — ,

fixed-axis rotation,

, – . . ,

force (F) and, – . ,

free-body diagrams for, –

impact (eccentric). ,

impulse. –

instantaneous center (IC) of zero

velocity. ,

kinematics, – . , –

kinetic diagrams for. –

kinetic energy and. ,

,

kinetics, –

linear momentum. , –

moment of inertia ( ) for, — .

, – .

momentum. —

normal component (n) coordinates,

osculating plane and,

particles, – Index

paths of,

position (r) and. ,

potential energy (V) of, ^ ,

principle of work and energy,

,

principles of impulse and

momentum,

procedures for analysis of,

,

,

relative-motion analysis,

,

rigid bodies,

, –

rotating axes,

rotation and,

,

rotational equation of motion,

,

tangential component (r)

coordinates, –

time derivatives for,

translation,

,

translation and rotation,

, –

translational equation of motion,

,

velocity (v) and. ,

, – –

work (t/) and. –

Plane of contact,

Plastic (inelastic) impact,

Polar coordinates, . See also

Cylindrical coordinates

Position. ,

,

,

angular ( ),

base point,

continuous motion and,

curvilinear motion and,

displacement (d) from changes of,

,

erratic motion and, –

fixed reference frame,

graphs of variables,

instantaneous center (IC) of zero

velocity, –

kinematics of particles and,

,

magnitude and,

planar kinematics of rigid bodies

and,

rectangular components,

rectilinear kinematics and,

,

relative-motion analysis and,

, — ,

relative vector, –

rotating axes,

rotation about fixed axis,

three-dimensional rigid-body

motion,

time (f),as a function of,

translating axes,

translating reference frame,

translation and,

vector (r),

,

velocity (v) as a function of. ,

Position coordinates ( ), — ,

dependent-motion analysis using,

- .

equations for,

kinematics of particles and,

,

origin (O),

procedure for analysis using,

rectilinear kinematics,

time derivatives and,

Potential energy (V),

,

conservation of energy and,

,

conservative forces and. ,

,

elastic,

equations for conservation of,

gravitational,

kinetic energy and, –

kinetics of a particle,

potential function for, –

procedure for analysis of,

rigid-body planar motion, — ,

spring force and,

weight (W), displacement of,

,

work (U) and,

,

Power (P),

average,

efficiency (e) and,

energy (£) and,

instantaneous,

procedure for analysis of,

units of,

Power-flight trajectory,

Power-series expansions,

Precession (<£), – . –

Principal moments of inertia ( ),

Principal normal axis,

Principle axes of inertia (Z),

,

Principle of impulse and momentum,

,

,

angular impulse, –

angular impulse and momentum.

,

angular momentum (H),

,

conservation of angular momentum.

diagrams for,

external and internal forces,

graphs for,

impact and,

kinetics of a particle,

, —

linear,

procedures for analysis using,

,

rigid-body planar motion,

scalar formulation,

systems of particles, –

three-dimensional rigid-body

motion,

time (r) and, –

vector formulation,

Principle of work and energy,

,

deformation and, –

displacement and,

equation for,

kinetic energy and,

,

kinetics of a particle,

procedures for analysis using,

rigid-body planar motion,

Index

Principle of work and energy

(Continued)

three-dimensional rigid bodies,

systems of particles, –

units of,

w ork of friction caused by sliding,

Problem solving procedure,

Products of inertia,

Projectile motion,

horizontal, –

particle kinematics and,

procedure for analysis of,

vertical, –

Propulsion (mass gain and loss),

, . also Control

volume

Q

Quadratic formula,

R

Radial component (vr),

Radial coordinate (r), –

Radius of curvature (p),

Radius of gyration,

Rectangular (x, y, z) coordinates,

,

acceleration (a), –

angular momentum (II) and,

curvilinear motion,

dot notation for,

equations of motion and,

kinematics of a particle,

kinetics of a particle,

position vector,

procedures for analysis using,

three-dimensional rigid-plane

motion and,

velocity (v), –

Rectilinear kinematics,

acceleration (a),

continuous motion, –

displacement (A),

erratic motion, –

graphs for solution of,

particles and,

position ( ),

procedure for analysis of,

sign conventions for, –

time (z) and,

velocity (v),

Rectilinear motion,

Rectilinear translation,

,

Reference frames, –

,

,

, –

acceleration (a), –

angular momentum (H) and, –

circular path, –

curvilinear motion, –

coordinating fixed and translating

axes,

equations of motion and,

, –

fixed,

inertial,

instantaneous axis of rotation,

,

kinematics of particles,

, –

kinetic energy, –

kinetics of particles,

Newtonian inertial, –

relative-motion analysis,

, –

rigid-body planar motion,

, –

rotation about a fixed axis, –

rotational motion, –

three-dimensional rigid-body

motion, –

translation and rotation,

translational motion,

translating,

translating-rotating systems. –

symmetry of, –

velocity (v), –

Relative acceleration,

Relative-motion analysis,

,

,

acceleration (a) and,

,

circular motion,

,

circular path,

coordinate systems for, — ,

,

coordinating fixed and translating

reference frames,

,

displacement and,

instantaneous center (IC) of zero

velocity,

kinematics of a particle,

pinned-end members,

, –

position vectors (r) and,

,

procedures for analysis using,

,

rigid-body planar motion,

,

rolling without slipping,

rotating axes,

rotation and,

three-dimensional rigid-body

motion,

translating axes,

,

translating reference frames,

,

translation and rotation,

, –

velocity (v) and,

,

Relative-position vector,

Relative velocity,

Resonance, –

Restitution, –

central impact and, –

coefficient (e) of, –

conservation of angular momentum

for, –

deformation and, –

eccentric impact and, –

elastic impact and,

impact and, –

impulse,

oblique impact and,

period of,

plastic impact and,

rigid-body planar motion, –

Resultant force,

Resultant vector, Index

Retrograde precession,

Right-hand rule,

Rigid bodies,

, –

absolute motion analysis, – L

acceleration (a) and, –

,

,

angular momentum,

,

,

angular motion, –

circular motion,

, –

circular path, — ,

conservation of energy,

conservation of momentum,

,

coordinating fixed and translating

reference frames,

,

couple moment (Af) in,

displacement (d) of,

,

eccentric impact of,

energy (E) and, –

equations of motion for,

,

,

fixed-axis rotation,

,

fixed-point rotation,

force (F) and,

free-body diagrams for, –

general plane motion,

,

general three-dimensional motion,

,

gyroscopic motion,

impact of,

impulse,

inertia and,

instantaneous center (IC) of zero

velocity,

kinematics of, –

kinetic energy and,

,

kinetics of, — ,

, –

linear momentum, –

moments of inertia ( ) for,

, –

momentum, — ,

pinned-end members,

, –

planar motion,

position (r),

,

potential energy (V) of,

products of inertia ( ) of, –

principle of impulse and

momentum,

principle of work and energy,

,

procedures for analysis of,

,

,

relative-motion analysis,

,

,

rolling without slipping,

rotating axes,

rotation and translation, –

rotation of,

,

rotational equations of motion,

,

,

systems of particles and,

systems of bodies and,

three-dimensional, –

time derivatives for, –

torque-free motion,

translating axes,

,

translation of,

,

translational equations of motion,

,

velocity (v),

,

,

work ( ) and, –

zero velocity,

Rolling without slipping,

Rotating axes,

,

acceleration (a) of,

,

instantaneous axis of rotation,

,

Coriolis acceleration of,

direction of,

fixed reference frame, –

magnitude, change of,

position vectors (r) for,

procedure for analysis of,

relative-motion analysis for,

,

rigid-body planar motion,

three-dimensional motion and,

,

time derivatives for, –

translating-rotating systems,

velocity (v) of,

Rotation,

,

,

absolute motion analysis,

acceleration (a) and,

angular momentum and,

angular motion and,

, –

circular motion and,

, –

circular path,

coordinating fixed and translating

reference frames,

deceleration,

displacement (d) and,

Euler’s theorem for,

finite,

fixed-axis,

,

fixed-point,

general planar motion for, –

general three-dimensional motion,

impulse and momentum of,

infinitesimal,

instantaneous axis of,

instantaneous center (IC) of zero

velocity,

kinetic energy and,

linear momentum and,

line of action,

paths of,

position (r) and, – Index

Rotation (Gwiwd)

procedures for analysis ot ,

,

relative-motion analysis,

,

right-hand rule for,

rigid-body planar motion and,

,

,

rotating and translating axes,

three-dimensional rigid bodies,

,

time derivatives for, –

translation and, –

velocity (v) and,

Rotational equations of motion,

,

,

acceleration (a) and,

,

center of mass (G) for, –

fixed axes,

fixed point, –

force (F) and,

inertial reference frame for,

, –

kinetic energy and,

kinetic moments,

moment equation about point ,

moment of inertia,

procedure for analysis of,

rigid-body planar motion,

,

three-dimensional rigid-body

motion,

time derivative for,

symmetry of reference frames for,

‘

S

s-f (position-time) graphs, –

Scalar formulation of angular

momentum,

Separation points of contact after

impact,

Shell elements, moment of inertia of,

Simple harmonic motion,

Slab in inertial reference frame,

Sliding, –

acceleration (a) and, –

position and,

principle of work and energy for,

procedure for analysis of,

relative-motion analysis for, –

velocity (v) and, –

work of friction by,

Slipping,

circular motion and,

equations of motion and,

forces that do no work,

general plane motion,

moment of inertia and,

relative-motion analysis and,

rigid-body planar motion,

,

rolling without,

zero velocity and,

Space cone,

Space mechanics,

,

,

areal velocity,

central-force motion and,

circular orbit,

control volume of particles, –

drag force,

eccentricity (e) of,

elliptical orbit, –

free-flight trajectory,

gravitational attraction (G) and,

inertia ( ) and, –

Kepler’s laws,

kinetics of a particle,

mass flow, –

orbital revolution,

parabolic path,

parallel-axis and parallel-plane

theorems for, –

power-flight trajectory,

precession (<£), –

principle of impulse and

momentum for,

propulsion (mass gain and loss),

,

spin (VO, –

three-dimensional rigid-body

motion and,

,

thrust,

torque-free motion,

trajectories, –

Speed, . See also

Acceleration; Magnitude

Spheres,fixed-point rotation and,

Spin (VO, –

Spinning axes, equations of motion

for, –

Spring force,

,

conservation of energy and,

conservative force of,

displacement by,

elastic potential energy and,

,

equations of motion for,

kinetics of a particle,

, –

potential function for, –

rigid-body planar motion,

vibrations and, –

weight and, –

work (U) of,

,

Statics,study of,

Steady flow,

control volume, –

fluid streams,

linear impulse and momentum.

procedure for analysis of,

Steady-state vibration, –

Symmetrical spinning axes,see

Gyroscopic motion

Systems, –

,

,

, –

angular impulse of, –

angular momentum of, –

angular motion of, –

center of mass (G),

connected bodies, Index

conservation of angular momentum,

conservation of energy,

conservation of linear momentum,

conservative forces and,

critically damped,

deformation in bodies, –

equations of motion for,

external and internal forces of,

,

fixed, –

kinetic energy and,

kinetics of a particle,

,

, –

mass flow,

mass gain and loss (propulsion),

,

moment of a force,

nonrigid bodies, –

overdamped,

potential energy (V) and,

principles of impulse and

momentum for, — , –

principle of work and energy for,

procedure for analysis of,

rigid bodies, –

sliding and,

time derivatives for, –

translating-rotating, –

underdamped,

vibration, –

work of friction and,

T

Tangential (r) coordinates,

, –

acceleration (a) and,

, –

circular motion components,

curvilinear motion components,

equations of motion and. ,

kinematics, –

kinetics,

particles,

planar motion and, –

procedure for analysis of,

rigid-body planar motion, –

rotation about a fixed axis, –

three-dimensional motion,

velocity (v) and,

Tangential force,

Three-dimensional motion,

, –

angular, –

angular momentum of,

angular velocity of, –

binormal axis,

curvilinear,

displacement from, –

equations of motion for,

Euler’s equations for, –

Euler’s theorem for,

fixed-axis motion, –

fixed-point rotation,

frames of reference for,

general,

gyroscopic motion,

,

inertia, moments and products of,

,

inertial frame of reference for,

kinematics of, –

kinetic energy of,

kinetics of, –

particles,

principle normal axis,

principle of impulse and

momentum,

principle of work and energy of,

,

procedures for analysis of,

rectangular (_r, y, z) coordinates,

relative-motion analysis of,

rigid bodies, –

rotating axes,

symmetrical spinning axes, –

time derivatives for, —

torque-free motion,

translating axes, –

translating coordinate systems for,

translating-rotating systems,

,

Thrust,

Time (z),

,

acceleration (a) as a function of,

continuous motion and,

curvilinear motion and,

cycle,

erratic motion and, –

graphs of variables,

linear impulse and momentum as a

functions of, –

orbital revolution,

period,

position (s) as a function of,

principle of impulse and

momentum and, –

rectilinear kinematics and,

velocity (v) as a function of,

vibration and,

Time derivatives,

,

,

absolute dependent motion analysis

using,

angular motion, –

conservation of energy and.

,

curvilinear motion, — ,

fixed-point rotation, –

rigid-body planar motion,

rotational equations of motion

using,

three-dimensional rigid-body

motion,

time-differential equations,

translating-rotating systems, –

vibration,

Torque-free motion,

Trajectories,

central-force motion of,

circular orbit,

eccentricity (e) of,

elliptical orbit, –

escape velocity of,

free-flight,

gravitational attraction (G) and,

hyperbolic,

orbital, –

parabolic path,

power-flight,

space mechanics, Index

Transient state of vibration,

Translating axes,

,

acceleration (a),

angular motion and, –

kinematics of particles,

observers (fixed and translating),

,

position coordinates for,

position vectors (r) for,

procedures for analysis of,

,

relative-motion analysis of,

,

,

rigid-body planar motion,

,

rotation and,

three-dimensional rigid bodies,

,

time derivatives for systems,

translating reference frames, –

translating-rotating systems,

velocity (v) of,

Translating coordinate systems,

,

Translating observer,

Translating reference frames, — ,

,

Translation, –

,

,

absolute motion analysis,

acceleration (a) and,

,

angular momentum and,

circular motion and, –

coordinate system axes,

,

coordinating fixed and translating

reference frames,

curvilinear,

displacement (r) and, –

impulse and momentum,

kinetic energy and,

linear momentum and,

paths of,

position vectors (r),

procedures for analysis of ,

rectilinear, — ,

relative-motion analysis,

,

rigid-body planar motion,

,

,

rotating axes with,

rotation and,

time derivatives for,

velocity (v) and,

,

Translational equations of motion,

,

acceleration (a) for,

curvilinear translation,

,

force (F) for,

kinetic energy and. ,

procedure for analysis using,

rectilinear translation,

rigid-bodv planar motion,

,

symmetry of reference frames for,

**three-dimensional rigid-bodymotion,Transverse component (¥^,Transverse coordinate ( ), –Trigonometric identities,UUnbalanced force,Undamped vibrations,,amplitude of,displacement and, –equilibrium position for,**

forcing frequency (w ) for,

**forced,free,frequency (f) of,frequency ratio,natural frequency (o?n) for,,period of,periodic force and, –periodic support displacement of,phase angle (<£),procedure for analysis of,resonance,simple harmonic motion of,spring force and, –Underdamped vibration systems,Unit vectors,Vv-s (velocity-position) graphs,v-r (velocity-time) graphs, –Variable force, work of,Vector analysis, –Vector formulation of angularmomentum,Vector functions,Vector of forces,Vector quantity, particle position anddisplacement as,Velocity (v),,, ^,,, –absolute,acceleration (a) and,angular (w),**

areal,

average,

central-force motion and, –

circular motion and, –

continuous motion and, –

coordinating fixed and translating

reference frames,

curvilinear motion and,

,

cylindrical components and,

direction and,

erratic motion and, –

escape,

fixed-axis rotation and,

fixed-point rotation and, –

forces doing no work,

graphs of variables, – .

gyroscopic motion and, –

instantaneous,

instantaneous center (IC) of zero,

,

kinematics of particles and,

,

magnitude of,

, Index

normal component (w) coordinates,

.

position (r) and. , –

position (s), as a function of,

procedures for analysis of,

radial component (vr),

rectangular components and. –

rectilinear kinematics and, – .

**.**

relative, . –

relative-motion analysis and. ,

, .

rigid-body planar motion. ,

,

, –

rolling without slipping,

rotating axis,

rotation and, . –

sign convention for,

slipping and. ,

space mechanics, –

speed (magnitude),

tangential component (f)

coordinates, .

three-dimensional rigid-body

motion, . –

time (f), as a function of,

time derivative for,

translating axes and, – . .

translating observer of.

translation and. .

translation and rotation. ,

transverse component (v^),

zero, . ,

Vertical displacement (A). ,

Vertical projectile motion. –

Vibrations, –

amplitude of,

complementary solution for.

critically damped systems,

cycle.

damped, . , –

displacement and. –

electrical circuit analogs and,

energy methods for conservation of

equilibrium position for,

forced, . ,

forcing frequency (to ), — .

free. , – .

frequency (/). ,

frequency ratio,

magnification factor (MF) for.

natural frequency (cg„). ,

overdamped systems,

particular solution for, –

period of time.

periodic force and, –

periodic support displacement of.

phase angle (^),

procedures for analysis of .

resonance. , –

simple harmonic motion of

spring force and, –

steady-state of. –

transient state of,

undamped forced,

undamped free. ,

underdamped systems.

viscous damped, – . —

Viscous damped vibration. ,

coefficient of damping.

critically damped systems.

damping force,

forced,

free. ,

overdamped systems,

steady-state. –

underdamped systems.

Viscous damping force. ,

Volume elements, integration of

moments of inertia using, –

Volumetric flow (discharge).

W

Watt (W), unit of

Weight (W),

conservation of energy and,

conservative forces and,

constant,

displacement of , – .

gravitational attraction and.

gravitational potential energy of

mass gain and loss,

mass of a body and. Ill

potential energy ( V) and,

potential function for, –

spring force and. –

vertical displacement of,

work (U) of a. ,

Work (LZ), – . .

conservation of energy and.

conservative forces and.

constant force, . .

couple moment ( ), of a,

deformation and, –

displacement and (d),

energy (E) and. , – .

external.

force (F) as,

friction caused by sliding.

internal,

kinetic energy and,

kinetics of a particle. –

nonconservative forces and.

potential energy (V) and,

potential function for, –

principle of energy and. ,

procedures for analysis of, . ,

rigid-body planar motion, –

slipping (no work).

spring force as,

system of particles. –

three-dimensional rigid body

motion,

units of

variable force, of a,

weight ( W) as,

zero velocity and (no work), Index

z

Zero velocity,

**general plane motion,instantaneous axis of, rigid-body planar motion,instantaneous center (IC) of,, rolling without slipping,procedure for analysis of, slipping (no work) and.relative-motion analysis,**

**كلمة سر فك الضغط : books-world.netThe Unzip Password : books-world.net**

### تحميل

يجب عليك التسجيل في الموقع لكي تتمكن من التحميل

تسجيل | تسجيل الدخول