Two objects of masses m and M move in circular orbits that have the same center. The force that gives rise to this motion is a force of attraction between the two objects acting along the line joining them. Use conservation of momentum and N's 2nd Law to show that they move with the same angular speed. Calculate the ratio of the radii of the orbits.(adsbygoogle = window.adsbygoogle || []).push({});

My attempt:

Conservation of Momentum

mv_{1}+Mv_{2}=C

N's 2nd Law

F_{net}=ma

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.

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# Calculate the ratio of the radii of the orbits

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