Question

For a planet moving in an elliptical orbit, why is (1/2)*I*w^2 not the correct expression for its kinetic energy?

Answer 1

The energy of rotation is given by 1/2Iw², but the total kinetic energy is the energy of rotation plus the energy of rotation. So, the kinetic energy is 1/2m(v²+r²w²), where w is the angular velocity and v is the velocity to increase or decrese distance to the center bdy. If we're on a circular orbit, v²=0.

Answer 2

V=ωxR (vectors)
ω=RxV/|R^2| (vectors)
so
ω=R*V*sinθ/R^2
ω=V*sinθ/R