A uniform solid disk of mass and radius rests on a perfectly smooth horizontal surface
PHYSICS · Multi-part · AP · Physics C: Mechanics · Torque and Rotational Dynamics · Torque and Rotational Dynamics
Problem
A uniform solid disk of mass 2.0kg and radius 0.30m rests on a perfectly smooth horizontal surface. The disk can slide without friction as well as rotate about its center.
Three separate force situations (Cases I–III) are applied for the same 0.50s time interval:
• Case I: A single horizontal force of 6.0N acts at the center of the disk, directed to the right.
• Case II: Two horizontal forces, each of 6.0N, act simultaneously: one at the center to the right and one at the rim to the left, tangent to the rim.
• Case III: Two horizontal forces, each of 6.0N, act at opposite ends of a diameter, tangent to the rim and in opposite directions (forming a pure couple).
Ignore any forces not explicitly mentioned.
(1) For each case, indicate whether the disk is in translational equilibrium during the interval. Justify qualitatively.
(2) For each case, indicate whether the disk is in rotational equilibrium during the interval. Justify qualitatively.
(3) Rank the three cases according to the magnitude of the disk’s center-of-mass acceleration, from greatest to least. Briefly explain your reasoning.
(4) Rank the three cases according to the magnitude of the disk’s angular acceleration, from greatest to least. Briefly explain your reasoning.