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.
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.