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**1. Homework Statement**

There is a point particle on the edge of a merry-go-round. It has mass 15kg and the merry-go-round has mass 235kg. The initial angular momentum is 2 radians per second. If the point particle moves from the outer edge of the merry-go round to the centre, what is the final angular momentum?

I've tried to do this problem using conservation of angular momentum and conservation of rotational kinetic energy and I get two different answers...

**2. Homework Equations**

moment of inertia of particle, I

_{p}= mr

^{2}and of merry-go-round, I

_{m}=mr

^{2}/2

rotational kinetic energy =Iω

^{2}/2

Angular momentum, L=Iω for particle or

**3. The Attempt at a Solution**

In both cases, the moment of inertia of the partcle in the centre is zero and therefore its rotational kinetic energy and angular momentum are zero .

First, using conservation of angular momentum,

intial angular momentum of merry go round + of particle = final angular momentum of merry-go-round.

0.5x235xr

^{2}x2 + 15xr

^{2}x2 = 0.5x235xr

^{2}xω

_{final}

235 + 30 = 0.5x235xω

_{final}

ω

_{final}= 2.2553.....

Using conservation of rotational kinetic energy,

0.5x15xr

^{2}x2

^{2}+ 0.5x0.5x235xr

^{2}x2

^{2}= 0.5x0.5x235xω

_{final}

^{2}

Then I get ω

_{final}= 2.1238....

I have a feeling that the issue may be that the rotational KE of the particle isn't zero even when it is at the centre, although I'm not sure...

Thank you in advance! :)