A solid wheel initially spinning clockwise (CW) is subjected to a…

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

A solid wheel initially spinning clockwise (CW) is subjected to a braking-and-boosting device that produces the following angular-acceleration profile: • For 0 s≤t<2 s0\,\text{s} \le t < 2\,\text{s}, α=+3 rad/s2\alpha = +3\,\text{rad/s}^2 • For 2 s≤t<5 s2\,\text{s} \le t < 5\,\text{s}, α=0\alpha = 0 • For 5 s≤t≤8 s5\,\text{s} \le t \le 8\,\text{s}, α=−2 rad/s2\alpha = -2\,\text{rad/s}^2 At t=0 st = 0\,\text{s} the wheel’s angular velocity is ω0=−3 rad/s\omega_0 = -3\,\text{rad/s} (negative indicates CW). Counter-clockwise is defined as positive. (a) Determine the angular velocity of the wheel at t=2 st = 2\,\text{s}, at t=5 st = 5\,\text{s}, and at t=8 st = 8\,\text{s}. Show all reasoning. (b) Calculate the wheel’s total angular displacement Δθ\Delta\theta from t=0 st = 0\,\text{s} to t=8 st = 8\,\text{s}. (c) During the 0–8 s interval, does the wheel ever reverse its direction of rotation? If so, at what time? Support your answer quantitatively.

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