A small child runs and jumps onto a merry-go-round which has a moment of inertia
ID: 1552378 • Letter: A
Question
A small child runs and jumps onto a merry-go-round which has a moment of inertia I_0 about its axis of rotation. The child has mass m and is initially moving with velocity v; she grabs onto a bar attached to the plate which is a distance R from the center of the merry-go-round. The merry go round was initially not rotating. Assume that the child is running tangential to the merry-go-round before jumping on as shown, What is the magnitude of the final angular velocity of the merry-go-round, omega_final? Give your answer in terms of m, v, R and I_0.Explanation / Answer
initial angular momentum of the system Li = m*v*R
final angualr momentum Lf = (I0 + m*R^2)*wfinal
from conservation of angular momentum Lf = Li
(I0 + m*R^2)*wfinal = m*v*R
wfinal = m*v*R/(I0 + m*R^2)