1. Rotational Energy

2. Goal of the class To understand rotational energy
Question of the day: What is the power of delivered by a torque?

3. Work Done by Torque
In the linear case we know how to calculate the work done:
Show the W = Int (τdθ)
But τ=Iα and α=dω/dt
So W = I int (ωdω) = ½ Iω2 =Krot

4. Conservation of Mechanical Energy
Work done by F = -ΔU = KE
Work done by τ = KErot
Ki+Ui=Kf+Uf

5. Power Delivered by Torque
Power delivered by force,
Dw = F.dr
P=dW/dt = F.dr/dt
dW =τdθ
P=τω

6. Example
A uniform solid disc of mass M and radius R is free to rotate about a frictionless pivot through the point P on its rim, as shown. The disc is released from rest where PQ is horizontal. What is the speed v of the point Q when PQ is vertical?
Ki+Ui=Kf+Uf
0+MgL/2 = ½ Iω2
For rod I=ML2/3
ω2 = 3g/L
Speed of free end v=Lω

7. Conservation of Angular Momentum
I1w1 = I2w2

8. 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

9. Homework
P365
Questions 4, 16, 44, 74, 80, 98