A solid disk of radius is mounted so that it can rotate freely about its central axis
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A solid disk of radius R is mounted so that it can rotate freely about its central axis. Two identical spring scales are attached to opposite sides of the disk’s rim at diametrically opposite points (points A and B). Each scale is oriented tangentially and can pull either clockwise or counter-clockwise. The setup is to be used to test whether the disk is in rotational equilibrium when different forces are applied.
(a) Sketch a clear labeled diagram of the disk showing points A and B, the pivot axis, and the directions of the forces that the spring scales could exert.
(b) Derive an algebraic expression for the net torque on the disk in terms of the magnitudes of the forces FA and FB read on the two spring scales and any relevant geometric quantities.
(c) The class plans to collect simultaneous readings of FA and FB for several trials and to graph net torque versus time to assess equilibrium. Describe—in words—what features of the graph would provide convincing evidence that the disk is in rotational equilibrium. Explain why these features correspond to the required physical condition.
(d) Propose one modification to the experimental design that would allow the students to reduce systematic error in their assessment of rotational equilibrium. Justify how your proposed change addresses a specific limitation of the original setup.