A student investigates a solid wheel of unknown mass by measuring its rotational…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics
Problem
A student investigates a solid wheel of unknown mass by measuring its rotational inertia about several parallel axes that are perpendicular to the wheel’s plane. Each axis is located a distance d from the wheel’s geometric center. The measured data are shown in the table.
Numerical data table:
d (m) 0.00 0.03 0.06 0.09
I′ (kg·m²) 0.220 0.229 0.256 0.301
(a) Plot the measured rotational inertia I′ as a function of d2 (a sketch with labeled axes is sufficient). Using any two of the data points, determine the slope and the vertical intercept of the best-fit straight line.
(b) Interpret the physical meaning of the slope and of the intercept obtained in part (a). Hence determine the wheel’s mass and its rotational inertia about the central axis.
(c) Suppose additional measurements at larger values of d begin to deviate systematically above the straight-line trend. Provide one plausible physical explanation for this behavior.