A bicycle wheel mounted on a low-friction axle is free to rotate about its central axis

PHYSICS · Multi-part · AP · Physics C: Mechanics · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

A bicycle wheel mounted on a low-friction axle is free to rotate about its central axis. The rim is marked with a reference line so its angular position can be measured relative to a fixed spoke. Initially (t=0t=0) the reference line is at θi=−1.2 rad\theta_i = -1.2\,\text{rad} (where the negative sign indicates a clockwise position relative to the spoke). The wheel is set into motion and, for the first 6.0 s6.0\,\text{s}, its angular velocity is observed to increase uniformly from ωi=2.0 rad s−1\omega_i = 2.0\,\text{rad}\,\text{s}^{-1} to ωf=6.0 rad s−1\omega_f = 6.0\,\text{rad}\,\text{s}^{-1}. (a) Calculate the angular displacement Δθ\Delta\theta of the wheel during the 6.0 s6.0\,\text{s} interval. (b) Determine the wheel’s angular position θf\theta_f at t=6.0 st = 6.0\,\text{s}. (c) Compute the average angular acceleration of the wheel over this interval and state its sign.

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