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Show that (R X P) . (R X P) = (RP)^2 - (R . P)^2. Assume the vectors R and P lie on the xy-plane. Use this result to express the kinetic energy of a particle in terms of the momentum in the radial direction and of the square of the angular momentum.

I have already showed that the above is true. The problem is that I don't know how to use this result for the kinetic energy equation.(I'm not even sure this is the equation that I must use since the problem doesn't say anything about how the particle moves)

K = 1/2 mv^2 + 1/2 Iw^2.

I'm not even sure what the momentum in the radial direction is.

As you can see, I'm having a little trouble here, but I think it should be easy. Thanks a lot for any help.