dynamics hibbeler chapter 12 notes

8/12/2019 Dynamics Hibbeler Chapter 12 Notes

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Engineering Mechanics: Dynamics

Chapter 12 Kinematics of a Particle

12.1 INTRODUCTION

Mechanics

a branch of physical science that is concerned with the state of rest and motion of bodies subjected toaction of forces

1. Staticsa. Concerned with the equilibrium of a body that is either at rest or moves with constant velocity

2. Dynamicsa. Concerned with bodies that have accelerated motionb. Kinematics

The study of the geometry of the motionc. Kinetics

The study of the forces that cause the motion12.2 RECTILINEAR KINEMATICS: CONTINOUS MOTION

Rectilinear

Straight-line pathRectilinear Kinematics

Kinematics of particles are characterized by position, velocity, and acceleration at any given instant ina straight-line motion

Position

Location of particle along a single coordinate axisDisplacement

Change in position

Velocity

Average speed is total displacement divided by total time Average velocity is displacement divided by total time1. Average velocity

a. 2. Instantaneous velocity


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a. Acceleration

Acceleration is zero if velocity is constant ( ) A particle that is slowing down is decelerating A particle can have an acceleration and yet have zero velocity1. Average acceleration

a. 2. Instantaneous acceleration

a. Relationship between instantaneous velocity and instantaneous acceleration

Constant acceleration (ac)

Equations can be integrated to obtain formulas that relate ac, v, s, andt

1. Velocity as a function of timea.

2. Position as function of timea. ( )

3. Velocity as a function of positiona. ( ) ( )

( )


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12.3 RECTILINEAR KINEMATICS: ERRACTIC MOTION

Examples

Differentiate I

ntegrate


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12.4 GENERAL CURVILINEAR MOTION

Curvilinear

Curved path s Curvilinear motion can cause changes in both in magnitude and direction of position, velocity, and

acceleration

Position

Path as a function of () Designated by the position vector r

()Displacement

Distance along the curve

Velocity

Speed is the magnitude of v v is tangent to the path Average velocity is displacement divided by total time1. Average velocity

a. 2. Instantaneous velocity

a. 3. Speed

a.

Acceleration

Acceleration is zero if velocity is constant ( ) A particle can have an acceleration and yet have zero velocity


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Acceleration is tangent to the hodograph (curve) and not the path

1. Average accelerationa.

2. Instantaneous accelerationa.

12.5 CURVILINEAR MOTION: RECTANGULAR COMPONENTS (I, j, k)

Position

Particle at point (x, y, z) on the curved path s1. Position vector

a. 2. Magnitude of ra.

Velocity

1. Velocity vectora. () () () b.

2. Magnitude of velocitya.

Acceleration

1. Velocity vectorc. () () () d.

2. Magnitude of velocityb.


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12.6 MOTON OF A PROJECTILE

Constant downward acceleration ac 1. Horizontal Motion

a. Velocity as a function of time ()

b. Position as a function time ()

c. Velocity as a function of position ( ) ( ) ()

2. Vertical Motiona. Velocity as a function of time

() b. Position as a function time

() c. Velocity as a function of position

( ) ( ) () ( )


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12.7 CURVILINEAR MOTION: NORMAL AND TANGENTIAL COMPONENTS (n and t)

Planar Motion

Using n (normal) and t (tangent) to describemotion

uis used to designate a unit vector radius of curvature is

Velocity

Acceleration

1. a. The tangential component of acceleration

represents the time rate of change in the

magnitude of the velocity.

2. a. The normal component of acceleration represents the

time rate of change in the direction of the velocity

b. always acts toward the center of curvature (centripetal acceleration)3.

4.

5. Magnitude of acceleration


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12.8 CURVILINEAR MOTION: CYLINDRICAL COMPONENTS (r and )

12.9 ABSOLUTE DEPENDENT MOTION ANALYSIS OF TWO PARTICLES

Example 1

Position

Velocity

Acceleration

Example 2

Position

Velocity

Acceleration


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12.10 RELATIVE-MOTION OF TWO PARTICLES USING TRANSLATING AXES

Position

Absolute position of each particle, rAand rB, is measuredfrom the common fixed origin O

Particle Bmoves with particleAwith each having their own axis The axes of BandAare permitted to translate (move) relative

to the fixed axis of O

The position of Bis measured relative toAis denoted by the relative-position vector

rB/A

Velocity

Acceleration


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dynamics hibbeler chapter 12 notes

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