Question 1. A merry-go-round of radius R = 1.5 m has a moment of inertia of I = 175 kg m2. The merry go round is given an initial angular speed of 1.6 rad/s. Shortly after the merry go round begins rotating a cylindrical weight is dropped on the merry-go-round.
(a) The cylindrical weight has a mass of 120 kg and a radius of 0.50 m. Find the new angular speed of the merry-go-round if the cylinder is dropped in the middle (or center) of the merry-go-round.
(b) What is the translational speed of a point on the edge of the merry-go-round after the cylindrical mass has been dropped on the merry go round?
(c) What is the Rotational Kinetic Energy of the combination of the merry-go-round and cylindrical weight?
Question 2. A mass m hangs vertically while attached to a rope that is wrapped around a wheel of mass M and radius R. The spokes on the wheel are so light that their mass can be neglected and the entire wheel can be treated as a hoop..
(a.) Find an expression for the magnitude of the angular acceleration of the wheel?
(b) Find an expression for the magnitude of the Torque on the wheel?
(c) Find an expression for the speed of the mass in after it has descended a distance h?