A merry-go-round has a radius of 2.0 m and a moment of inertia 300 kg⋅m2. A boy of mass 50 kg runs tangent to the rim at a speed of 4.0 m/s and jumps on. If the merry-go-round is initially at rest, what is the angular velocity after the boy jumps on?
A star collapses which greatly increases its density. The -kg-mass of the star remains the same throughout the collapse, as does the star’s mass distribution, which is uniformly spherical. Before collapse, the star’s radius was km and it had a rotational period of 28 days. The star’s radius is km after the collapse, what is its rotational period? Consider a day to be equal to seconds.
A diver off the high board imparts an initial rotation to his fully extended body, goes into a tuck, executes three back somersaults, and then hits the water. His moment of inertia before the tuck is 16.9 kg⋅m2 and after the tuck during the somersaults is 4.2 kg⋅m2. What initial rotation rate must he impart to his body directly off the board and before going into the tuck if he takes 1.4 s to execute the somersaults before hitting the water?
Three children are riding on the edge of a merry-go-round that has a mass 100.0 kg, a 1.60-m radius, and is spinning at 20.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the child who has a mass of 28.0 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm?
Eight children, each of mass 40 kg, climb on a small merry-go-round. They position themselves evenly on the outer edge and join hands. The merry-go-round has a radius of 4.0 m and a moment of inertia kg⋅m2. After the merry-go-round is given an angular velocity of 6.0 rpm, the children walk inward and stop when they are 0.75 m from the axis of rotation. What is the new angular velocity of the merry-go-round? Assume there is negligible frictional torque on the structure.