Rotational Motion

Chapter 9: Rotational Motion

Rigid body instead of a particleRotational motion about a fixed axisRolling motion (without slipping)

Concepts of rotational motion

Rotational Motion

Angular QuantitiesKinematical variables to describe the rotational motion:Angular position, velocity and acceleration

)(

)(

)(

2

0 t

0 t

rad/s dt

d

t lim

rad/s dt

d

t lim

rad R

l

ave

ave

Rotational Motion

Angular Quantities: VectorKinematical variables to describe the rotational motion:Angular position, velocity and accelerationVector natures

x

y

z

R.-H. Rule

)(

)(

)(

2rad/s k dt

dkk

rad/s k dt

dkk

rad R

l

ˆˆlimˆ

ˆˆlimˆ

0

0

t

t

t

t

Rotational Motion

“R” from the Axis (O)

Solid Disk Solid Cylinder

Rotational Motion

Kinematical Equations for constant angular acceleration

constantNote

ax Conversion

:

)(

:

020

2

0

200

-2 (3)

(2)2

1 (1)

, ,

t

t t

v

Rotational Motion

College Physics: Motion along a Straight Line

On a merry-go-round, you decide to put your toddler on an animal that will have a small angular velocity. Which animal do you pick?

A. Any animal; they all have the same angular velocityB. One close to the hubC. One close to the rim

Rotational Motion

vtan= same = r11= r22

Tooth spacing is the same 2r1 N1

2r2 N2

=

2

1= N2

N1

Rotational Motion

=0.8 x50=40 m/s

=10^2x0.8=80m/s

w=10 rad/s3

Rotational Motion

Finding the moment of inertia for common shapes

Rotational Motion

Rotational Motion

Rotational Motion

9-36

Rotational Motion

Rotational Motion

Rotational Motion

Conservation of energy in a well

+0

Find the speed v of the bucket and the angular velocity w of the cylinder just as the bucket hits the water

Rotational Motion

Rotational Motion

Relationship between Linear and Angular Quantities

RR

R

Ra

Ra

Ra

R

Rl

l R

l

222

rad

tan

tan

( (3)

(2)

)(

(1)

)

d

d

d

d

v

v

v

v

tt

t

t like t )(

atan

arad