Problem with 2 cars on almost masless spining platform

[farolero]

Are you assuming that they are "coasting" through the turn, I.e. Doing 0 work with their legs?

Yes they are coasting and doing zero work with their legs.

 

[Dale]

Then assuming the skates are frictionless on the ice, kinetic energy is conserved. I believe that is the whole point of your setup. You want the skaters to turn while conserving kinetic energy.

So what unknowns do you have, and what constraints and conservation principles can you use?

 

[farolero]

I have to keep constant the initial kinetic energy which would be 0.5*200*1=100

And angular momentum that would be zero

So 0=mvr-Iw=200*v*1-iw=0
So 200v=Iw
So supposing the platform has such a shape as to have a moment of inertia equal to 2 then
200v=w

So now i balance energy:
100=0.5*200*v^2+1w^2
100=100v^2+w^2
so 100-100v^2=w^2
substituting:
100-100v^2=40000v^2
so 100=40100v^2
v=0.05 m/s
so w=100

Would this be correct?

 

[Dale]

The approach is correct. I haven't checked the arithmetic, but even if you made an error there you have the concept right.