At a bicycle repair shop, a bicycle tire of mass M and radius R is suspended from a peg on the wall. The moment of inertia of the tire around the peg is 2MR2. If the tire is displaced from equilibrium and starts swinging back and forth, what will be its frequency of oscillation?

Amachinist turns the power on to a grinding wheel, at rest, at time t = 0 s. the wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 96 rad/s. the wheel is run at that angular velocity for 40 s and then power is shut off. the wheel slows down uniformly at 1.5 rad/s2 until the wheel stops. in this situation, the time interval of deceleration is closest to: