Heres a playground merrygoround of mass M and radius R with

Here\'s a playground merry-go-round, of mass M and radius R, with moment of inertia 1/2 M R^2. That\'s you standing on it, with mass m, and we\'re supposing you\'re very small, so we\'ll approximate you as a point mass. The merry-go-round starts out at rest, and then you jump off of it. Suppose you jump to the left, in a direction tangent to the edge of the merry-go-round, so that you\'re moving at a speed v relative to the ground. Find the angular velocity of the merry-go-round.

Solution

Here ,

moment of inertia , I = 0.5 M * R^2

let the angular velocity of merry go round is w

Using conservation of angular momentum

I * w - m* v * R = 0

0.5 * M * R^2 * w - m * v * R = 0

0.5 * M * R * w - m * v = 0

w = 2 * m * v/(M *R)

the angular velocity of the merry go round is 2 * m * v/(M *R)