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## Homework Statement

A child with mass m is standing at the edge of a merry go round having moment of inertia I, radius R and initial angular velocity x as shown. (The figure shows a disc moving anticlockwise, with the velocity v (Mentioned at the end) pointing upwards to the right most edge of the disc. ) The child jumps off the edge of the merry go round with tangential velocity v, w.r.t. the ground. The new angular velocity of the merry go round is.

## Homework Equations

Basic Rotational motion equations. Mainly rotational energy, and angular momentum.

## The Attempt at a Solution

The conservation of angular momentum yielded the correct result for the problem stated. But when I do this using conservation of energy it does not (I have missed something out, I need to know what). Here is what I have done.

0.5 * m *v^2 + 0.5 * I * y^2 = 0.5 (I + mr^2)*x^2

Taking y as the final angular momentum. The result is something else. The answer according the reference book is given as:

((I + mr^2)*x^2 - mvr)/I

Thank you for the support and all your help.