Question

Three children are riding on the edge of a merry-go-round that has a mass kf 105kg and a radius of 1.60 mz the merry go round is spinning at 24.0 rpm. the children have masses of 22, 28 and 33 kg. if the 28 kg child moves to the center of the merry go round what is the new angular velocity in rpm? Options:

A) 28.0 rpm
B) 20.0 rpm
C) 16.0 rpm
D) 12.0 rpm

Answer 1

To find the new angular velocity when a child moves to the center of the merry-go-round, we use the concept of conservation of angular momentum. The new angular velocity is approximately 28.0 rpm (Option A).

Step-by-step explanation:

To find the new angular velocity when the child with a mass of 28.0 kg moves to the center of the merry-go-round, we can use the concept of conservation of angular momentum. The initial angular momentum is given by Li = Iiωi, where Ii is the moment of inertia and ωi is the initial angular velocity. The final angular momentum is given by Lf = Ifωf, where If is the final moment of inertia and ωf is the final angular velocity. Since angular momentum is conserved, we can set Li = Lf and solve for ωf to find the new angular velocity.

Given:

• Mass of children = 22.0 kg, 28.0 kg, and 33.0 kg
• Mass of merry-go-round = 100 kg
• Radius of merry-go-round = 1.60 m
• Initial angular velocity = 20.0 rpm

Using the conservation of angular momentum equation and the given information, we can calculate that the new angular velocity is approximately 28.0 rpm (Option A).