A student is given a graph of the net torque on a rigid body as a function of its…
PHYSICS · Single correct · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A student is given a graph of the net torque τ on a rigid body as a function of its angular position θ. The student claims that the mechanical work done on the body as it turns from θ1 to θ2 can be found by calculating the area under the curve between those two positions. Which of the following statements provides the best justification for the student’s claim?
(a) Because τ has units of N·m and an angle in radians is dimensionless, the product τΔθ must have units of joules; therefore the area under a τ–vs–θ graph necessarily represents work or energy.
(b) For any small angular displacement dθ, the incremental work done is the product τdθ, so summing these products yields the total work as the area under the curve.
(c) Torque multiplied by angular displacement gives the power delivered during the motion, so integrating τ with respect to θ determines the total power supplied over the turn.
(d) Because the slope of a torque–versus–angle graph corresponds to the rate of change of torque, which equals Iα, taking the area under the graph yields the angular momentum change and therefore the work done.