PHY/EGR 321.001

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PHY/EGR 321.001. Spring 2008. Harry D. Downing. Professor and Chair Department of Physics and Astronomy. Roll Call. Fill out Student Information Sheets Pass out syllabi then go to next slide Take pictures of each student in lab today. Let’s visit the web for course information.

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### PHY/EGR 321.001

Spring 2008

Harry D. Downing

Professor and Chair

Department of Physics and Astronomy

Roll Call

Fill out Student Information Sheets

Pass out syllabi then go to next slide

Take pictures of each student in lab today

Let’s visit the webfor course information.

physics.sfasu.edu

Cover Page

Staple at 450

NAME

PHY/EGR 321.001

Date

Problems

Cover Page,Example

Staple at 450

Harry Downing

PHY/EGR 321.001

1-16-08

Ch 11 – 2, 6, 9, 16

Pass out some example

### CHAPTER 11

Kinematics of Particles

11.1 INTRODUCTION TO DYNAMICS
• Galileo and Newton (Galileo’s experiments led to Newton’s laws)
• Kinematics – study of motion
• Kinetics – the study of what causes changes in motion
• Dynamics is composed of kinematics and kinetics
11.2 POSITION, VELOCITY, AND ACCELERATION

For linear motion x marks the position of an object. Position units would be m, ft, etc.

Average velocity is

Velocity units would be in m/s, ft/s, etc.

The instantaneous velocity is

The average acceleration is

The units of acceleration would be m/s2, ft/s2, etc.

The instantaneous acceleration is

Notice

If v is a function of x, then

One more derivative

32

16

0

6

2

4

12

0

4

6

2

-12

-24

-36

12

4

6

2

0

-12

-24

Plotted

Consider the function

x(m)

t(s)

v(m/s)

t(s)

a(m/s2)

t(s)

11.3 DETERMINATION OF THEMOTION OF A PARTICLE

Three common classes of motion

with

then get

11.6 MOTION OF SEVERAL PARTICLES

When independent particles move along the same line,

independent equations exist for each.

Then one should use the same origin and time.

Relative motion of two particles.

The relative position of B with respect to A

The relative velocity of B with respect to A

xA

xB

A

E

F

B

G

C

D

Let’s look at the relationships.

System has one degree of freedom since only one coordinate can be chosen independently.

xC

xA

xB

C

A

B

System has 2 degrees of freedom.

Let’s look at the relationships.

y

x

z

CURVILINEAR MOTION OF PARTICLES

11.9 POSITION VECTOR, VELOCITY, AND ACCELERATION

P’

P

Let’s find the instantaneous velocity.

y

y

x

x

z

z

P’

P

y

y

y

x

x

x

z

z

z

P’

Note that the acceleration is not

necessarily along the direction of

the velocity.

P

Rate of Change of a Vector

The rate of change of a vector is the same with respect to a fixed frame and with respect to a frame in translation.

y

x

z

y

P

x

z

y

x

z

y

y’

x

x’

z

z’

11.12 MOTION RELATIVE TO A FRAME IN TRANSLATION

B

A

O

11.13 TANGENTIAL AND NORMAL COMPONENTS

Velocity is tangent to the path of a particle.

Acceleration is not necessarily in the same direction.

It is often convenient to express the acceleration in terms of components tangent and normal to the path of the particle.

y

x

O

Plane Motion of a Particle

P’

P

y

x

O

P’

P

y

x

O

Motion of a Particle in Space

The equations are the same.

P’

P

z

y

x