1. Rotational Energy

2. Goal of the class
To understand conservation of angular momentum and rolling motion
Question of the day: Which rolls down a slope faster, a cylinder or a sphere?

3. Conservation of Angular Momentum
I1w1 = I2w2

4. Conservation of Angular Momentum
No torque means dL/dt = 0
Therefore I1w1 = I2w2
Neutron star
T=10days Ri = 10,000km
Rf = 3km find Tf =9x10-7 days
Merry go round

5. Merry go Round Merry go round R=3m, M=200kg, wi = 2.1rad/s
m = 45 kg, starts at edge (3m) walks inwards so r=1m, wf = ?
Iw=iW
Ii = 1/2MR2 +mR2

6. Rolling Motion

7. Pure Rolling Motion
Rolling without slipping

8. Kinetic Energy Rotation Translation Combined
KErot = 1/2Iw2 KE = 1/2Mv2 KEroll =1/2 Ip w2
=1/2 (I + MD2) w2
=same as before

9. Cylinder Rolling down an Incline
Highlight they love this in AP exams
If sliding 1/2mv2 = mgh
Rolling you need 1/2Iw2 too.
Which rolls faster a sphere, a cylinder or a ring?