2. Rotational kinetic energy
Kinetic energy of a point object rotating about a center:
Write in terms of w:
Moment of inertia:
“rotational” mass
Demo: rod with masses, different for axes

3. Moment of inertia Axis C is perpendicular to the page
Like the different ways to rotate a sheet of paper
P1. Which has the largest I: for axis A, B or C?

4. Moment of inertia Axis C is perpendicular to the page
Like the different ways to rotate a sheet of paper
P1. Which has the largest I: for axis A, B or C?

5. Extended objects Axis C is perpendicular to the page
Parallel axis theorem: Each axis above is through the center of mass. If we rotate about a new axis parallel to it but displaced by h:
hoop about edge
rod about end

7. Linear-angular analogies
Newton’s second law for rotation
A rope pulls tangentially on a wheel. What angular acceleration a does this force cause?

8. P2. For the wheel on the right with the same mass, but twice the radius, what has happened to the moment of inertia I?
decreases by 4
decreases by 2
stay the same
increases by 2
increases by 4

9. P3. So what force F­2 is needed for the wheel on the right to give the same a as the wheel on the left?
0.25 N
0.5 N
1 N
2 N
4 N

10. Conservation of energy to find speeds
The ropes are wrapped around the flywheels (disks). How fast is the bucket moving after it has fallen h? R mb M r m

11. Racing objects rolling down incline
P4. Which kind of rolling object is moving the fastest at bottom of an incline (and wins!) when released from rest at the same height?
sphere B. disk C. hoop __________
Hint: they all have the same total KE at the end: linear + rotational. The one that wins has the most linear KE.

12. Objects rolling up incline
P5. Three objects have the same mass and R. If each rolling object is moving at the same speed v on flat ground, which object rolls highest up a slope?
A. sphere
B. disk
C. hoop
D. all the same

13. Yo-yo physics
What makes the yo-yo speed up?