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My attempt:

Conservation of Momentum

m

**v**

_{1}+M

**v**

_{2}=C

N's 2nd Law

**F**

_{net}=m

**a**

For uniform (I assume, because I know no better, rather than show that the motion is uniform - feel free to give me a lesson on that topic) circular motion: F=mv

^{2}/r

s=[the]r

ds/dt=v=d[the]/dt*r=wr

So, F=mrw

^{2}, for uniform circular motion

But since v=wr

mwr + MWR = K

dP/dt= mrw

^{2}+ MRW

^{2}=F1+F2=0

dP/dt=0=mr(dw/dt)+MR(dW/dt)

mr(dw/dt)+MR(dW/dt)= mrw

^{2}+ MRW

^{2}=0

mr(dw/dt-w^2)=MR(W^2-dW/dt)=0

dw/dt=w^2

dW/dt=W^2

And you may have thought I was going somewhere with that. But I'm not. No matter what I do to these equations I can't get w=W!

A little hint would be nice. Thank you.