كتاب Engineering Mechanics Statics and Dynamics 15th Edition

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Engineering Mechanics Statics and Dynamics 15th Edition
R. C. Hibbeler

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CONTENTS
General Principles
Chapter Objectives
J Mechanics
. Fundamental Concepts
Units of Measurement
. The International System of Units
. Numerical Calculations
. General Procedure for Analysis
Force Vectors
Chapter Objectives
. Scalars and Vectors
. Vector Operations
. Vector Addition of Forces
. Addition of a System of Coplanar
Forces
. Cartesian Vectors
. Addition of Cartesian Vectors
. Position Vectors
. Force Vector Directed Along a Line
. Dot Product
XIIIXIV Contents
Equilibrium of a
Particle ai
Chapter Objectives
. Condition for the Equilibrium
of a Particle
. The Free-Body Diagram
. Coplanar Force Systems
. Three-Dimensional Force Systems
Force System
Resultants
Chapter Objectives
. Moment of a Force—Scalar
Formulation
. Principle of Moments
. Cross Product
. Moment of a Force—Vector
Formulation
. Moment of a Force about a
Specified Axis
. Moment of a Couple
. Simplification of a Force and Couple
System
. Further Simplification of a Force and
Couple System
. Reduction of a Simple Distributed
Loading Contents xv
Equilibrium of a
Rigid Body
Chapter Objectives
. Conditions for Rigid-Body
Equilibrium
. Free-Body Diagrams
Equations of Equilibrium
. Two- and Three-Force Members
. Free-Body Diagrams
. Equations of Equilibrium
. Constraints and Statical Determinacy

Structural Analysis
Chapter Objectives
. Simple Trusses
. The Method of Joints
. Zero-Force Members
. The Method of Sections
. Space Trusses
. Frames and Machines XVI Contents
Internal Forces
Chapter Objectives
. Internal Loadings
. Shear and Moment Equations and
Diagrams
* 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

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