Question

A 50.0 kg child stands at the rim of a merry-go-round of radius 2.10 m, rotating with an angular speed of 3.35 rad/s. (a) What is the child's centripetal acceleration? m/s²

Answer 1

To find the new angular velocity when the child moves to the center of the merry-go-round, we need to use the conservation of angular momentum. Initially, the total angular momentum of the system is the sum of the individual angular momenta of the children. When the child with a mass of 28.0 kg moves to the center, their angular momentum becomes zero due to the decreased radius.

Step-by-step explanation:

To find the new angular velocity when the child moves to the center of the merry-go-round, we need to use the conservation of angular momentum. Initially, the total angular momentum of the system is the sum of the individual angular momenta of the children. When the child with a mass of 28.0 kg moves to the center, their angular momentum becomes zero due to the decreased radius. The new total angular momentum is then equal to the sum of the angular momenta of the other two children. Using the equation for angular momentum, we can calculate the new angular velocity by rearranging and solving for ω.