A solid sphere of radius R rotates with angular velocity $\omega$. A small beetle crawls from the pole to the equator with constant velocity v relative to the surface. The beetle stops at the equator. Calculate the change in the sphere's rotational kinetic energy, taking into account the relativistic mass of the beetle's lunch.
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: April, held separately for 9th, 10th, and 11th graders. russian physics olympiad problems pdf