A baseball pitcher throws the ball in a motion where there is rotation of the forearm about the elbow joint as well as other movements. If the linear velocity of the ball relative to the elbow joint is 20.3 20.3 m/s at a distance of 0.500 0.500 m from the joint and the moment of inertia of the forearm is 0.450 0.450 kg·m2, what is the rotational kinetic energy of the forearm?

Two masses are connected by a rope that hangs over a pulley as shown below. the pulley is a uniform cylinder of radius 푅=0.381meters and mass 푀=3.1푘푔. initially 푚"is on the ground and 푚#rests 2.5 meters above the ground. if the system is released, use conservation of energy to determine the speed of 푚#just before it strikes the ground. assume the pulley bearing is frictionless.