21. Angular Momentum - Galileo and Einstein

Yet Another Look at That Hoop…• Take no slipping, sov = Rω, a = Rα• Since there’s no slipping, thepoint on the hoop in contactwith the ramp is momentarilyat rest, and the hoop is rotatingabout that point.• The only torque about thatpoint is gravity—τ = mgRsinθ• The moment of inertia aboutthat point, from the parallelaxis theorem, is I CM + mR 2 =2mR 2 , so mgRsinθ = 2mR 2 α,and a = α/R = (gsinθ )/2.• xF frmgsinθ