1. Rotational Kinetic energy

2. Rotational Kinetic Energy
Rotational kinetic energy is the kinetic energy due to the rotation of an object about a fixed axis and it is part of the the object’s total kinetic energy.
Requirement: ω must be in rad/s
Unit: Joules
It can be useful to use
v = ωr or ω = v r

3. Rotational Kinetic Energy
When to use rotational kinetic energy
You are told an object is rolling
You are given the moment of inertia
You are asked about angular speed

4. Example
Starting from rest, a basketball rolls from the top of a hill to the bottom, reaching a translational speed of 7.34 m/s. Ignore frictional losses. I = 2/3 MR2
(a) What is the height of the hill?
(b) Released from rest at the same height, a can of frozen juice rolls to the bottom of the same hill. What is the translational speed of the frozen juice can when it reaches the bottom? I = ½ MR2

5. Example
A projectile launcher uses a spring with a spring constant of 500 N/m, to shoot a small solid, round ball of mass 100 grams and radius 2 cm across a room. The spring in the launcher is compressed 10 cm from its equilibrium position. The launcher is located on a level table. The table is 1.3 m in height. Rotational inertia for a solid sphere I = 2/5mr2
With what speed does the ball leave the end of the table?
(b) How long does it take the ball to reach the floor after leaving the table?
(c) Where on the floor does the projectile land?
(d) If the mass of the ball is increased, how would the landing distance be effected? Increase, decrease, stay the same. Justify your answer.

6. Rotational Kinetic Energy of a skater
When a figure skater moves her arms in closer to her body while spinning, what happens to the skater’s speed?
Increases, Decreases, stays the same
How does this affect her rotational kinetic energy?
Increases, decreases, stays the same
Where does the extra kinetic energy come from?

7. Rotational Kinetic Energy
Find the velocity of the following system (m1>m2) after it has moved through some height h. The pulley has mass M, radius R and I = MR2
V = sq rt (2 ((m1-m2)/(m1+m2+M))gh)