Activity 12.9.1. The Sliding Hoop.
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).
(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.
(b)
Calculate the distance the hoop slides before it is rolling without slipping. Assume you know the coefficients of friction.
Tip.
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.
