A hoop is launced up an incline with an initial translational speed vo as shown below. At some point, the friction of the inlcine will cause the hoop to roll. Find: a. The time at which the hoop begins to roll. b. The angle φ that minimizes the time for the hoop to roll.

A hoop is launced up an incline with an initial translational speed vo as shown below. At some point, the friction of the inlcine will cause the hoop to roll. Find: a. The time at which the hoop begins to roll. b. The angle φ that minimizes the time for the hoop to roll.

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Question

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A hoop is launced up an incline with an initial translational speed v_o as shown below. At some point, the friction of the inlcine will cause the hoop to roll. Find:
a. The time at which the hoop begins to roll.
b. The angle φ that minimizes the time for the hoop to roll.