A skateboard wheel is observed rolling along a level sidewalk without visibly sliding…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A skateboard wheel is observed rolling along a level sidewalk without visibly sliding against the concrete.
For the purposes of this question, treat the wheel as a uniform solid cylinder of radius r and mass M. Assume static friction is sufficient to prevent any slipping during the motion.
Provide qualitative explanations only; no numerical calculations are required.
(a) Describe the relationship between the speed of the wheel’s center of mass and its angular speed while it rolls without slipping. In your description, identify the physical reason this relationship must hold.
(b) Suppose the wheel’s angular speed remains unchanged but a larger–radius wheel is substituted in its place. Explain how the translational speed of the new wheel’s center of mass would compare with that of the original wheel.
(c) The wheel is then given a forward translational acceleration acm. Explain what must simultaneously happen to the wheel’s angular acceleration for rolling without slipping to continue, and justify your answer in terms of the contact point’s motion relative to the ground.
(d) If the wheel suddenly encounters a patch of sand so that it begins to slip, discuss qualitatively how the relationship you described in part (a) changes and what happens to the direction of the frictional force as a consequence.