Application: The Sliding Hoop

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Section 12.9 Application: The Sliding Hoop

Activity 12.9.1. The Sliding Hoop.

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SA hoop with mass $m$ and radius $r$ is thrown to the right with initial speed $v_i$ and initial angular speed $\omega_i$ such that the hoop is spinning backwards (opposite the direction it would need to spin to roll without slipping).

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(a)

After observing the hoop, give a qualitative explanation, including at least one extended free-body diagram, to account for the motion of the hoop.

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(b)

Calculate the distance the hoop slides before it is rolling without slipping. Assume you know the coefficients of friction.

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Hint.

Write down the Law of Motion (both translational and rotational) for the hoop and use it to calculate the amount of time the hoop travels before it rolls without slipping.

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