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Rotational Motion
Chapter 9: Rotational Motion
Rigid body instead of a particleRotational motion about a fixed axisRolling motion (without slipping)
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
Kinematical Equations for constant angular acceleration
constantNote
ax Conversion
:
)(
:
020
2
0
200
-2 (3)
(2)2
1 (1)
, ,
t
t t
v
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
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