A hoop, a solid cylinder, a solid sphere, and a thin spherical shell each have the same mass of 2.58 kg and the same radius of 0.184 m. Each is also rotating about its central axis with an angular speed of 42.0 rad/s. What is the magnitude of the angular momentum of each object? (Enter your answers in kg · m2/s.) (a) hoop b; solid cylinder  c; solid sphere  d; thin, spherical shell

A ball (in the form of a spherical shell which has a moment of inertia of 2/3 M R^2) rolls down a roof, then falls to the ground. The ball has a mass of 1.65 g and a radius of 15.0 cm. The roof is inclined at 20.0 degrees and the ball rolls a distance of 3 meters along the roof before falling off. a)  What is the angular speed of the ball at the moment it leaves the roof? b)  If the distance from the end of the roof to the ground is 2.50 m, how many revolutions does the ball make before it hits the ground?

A child jumps to the edge of a carousel, that is in the shape of a circular plate with a radius of 1.3 m and was rotating at an angular velocity of 1.2 s-1 before the chuld jumped on it. The weight of the carousels is 80 kg, the weight of the child is 22 kg. What is their angular velocity after the jump? Later, the child moves closer to the center of the carousel plate by 80 cm. What is the new angular velocity?

A playground merry-go-round of radius R = 1.80 m has a moment of inertia I = 255 kg. m² and is rotating at 12.0 rev/min about a frictionless vertical axle. Facing the axle, a 23.0-kg child hops onto the merry-go-round and manages to sit down on the edge. What is the new angular speed of the merry-go-round? rev/min