Rotational Energy

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

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

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

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

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

Conservation of Angular Momentum I1w1 = I2w2

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

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