A student investigates two electric motors, A and B

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems

Problem

A student investigates two electric motors, A and B. Each motor applies a torque to a small flywheel. The torque exerted by each motor as a function of the flywheel’s angular position θ\theta is described below. • Motor A: From θ=0 rad\theta = 0\,\text{rad} to θ=4 rad\theta = 4\,\text{rad} the torque is constant at 0.40 N⋅m0.40\,\text{N}\cdot\text{m}. • Motor B: From θ=0 rad\theta = 0\,\text{rad} to θ=2 rad\theta = 2\,\text{rad} the torque is 0.70 N⋅m0.70\,\text{N}\cdot\text{m}; from θ=2 rad\theta = 2\,\text{rad} to θ=4 rad\theta = 4\,\text{rad} the torque is 0.10 N⋅m0.10\,\text{N}\cdot\text{m}. No other external torques act on the flywheels during the 0 rad→4 rad0\,\text{rad} \rightarrow 4\,\text{rad} interval. (a) On the axes below, sketch qualitatively accurate torque–versus–θ\theta graphs for motors A and B over the interval θ=0 rad\theta = 0\,\text{rad} to θ=4 rad\theta = 4\,\text{rad}. Label numerical values on both axes. (Provide your sketch on your answer sheet.) (b) Using your graphs, determine the rotational work done on each flywheel during the interval. Show how information from the graph leads to your answers. (c) Compare the two motors in terms of the average energy transferred per radian of rotation over the interval. Explain what your comparison implies about the motors’ ability to accelerate identical flywheels starting from rest.

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