A hoop with a mass $m$ and unknown radius is rolling without slipping on a flat surface with an angular speed $\omega$. The hoop encounters a hill and continues to roll without slipping until it reaches a maximum height $h$.

Question

A hoop with a mass $m$ and unknown radius is rolling without slipping on a flat surface with an angular speed $\omega$. The hoop encounters a hill and continues to roll without slipping until it reaches a maximum height $h$.(a) Derive an expression for the radius of the hoop in terms of given quantities and fundamental constants.
, (b) What direction does friction point while the ball is rolling up the ramp? Explain your reasoning.
, (c) After reaching the maximum height, the ball begins to roll back down. What direction does friction point while the ball is rolling down the ramp? Explain your reasoning.
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Rachel · Accepted Answer

$ R = \sqrt{\frac{gh}{\omega^2}} $
Up the ramp.
Up the ramp.

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