Question

3. Potential energy of rings. You know that the gravitational potential energy of two interacting spherical masses (e g. Earth and Sun) s u--GMm, where r distance between their centers. If the masses are not spherical, this expression is not valid. However, we can still find the total potential energy by dividing the non-spherical mass into bits, treating each tiny bit as a point mass (which gravitates like a sphere), and adding their effects. That is, U-J -GMdm. This integral is evaluated using steps completely analogous to those we use to evaluate a moment of inertia integral. Throughout this problem, let us use the convention that the potential energy is 0 at infinite separation.

Answer 1

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