PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A uniform solid cylinder (mass 4.0kg, radius 0.15m) is mounted on a low-friction axle. Two external devices exert torques that vary with angular position according to the following table.
θ(rad): 0, 0.50, 1.0, 1.5, 2.0
τ1(N⋅m): 1.0, 1.0, 1.0, 0, 0
τ2(N⋅m): 0, 0.8, 1.2, 1.2, 0.8
(Sign convention: counter-clockwise positive; both torques are counter-clockwise.)
(a) Plotting is not required, but describe the qualitative shape of each torque-versus-θ curve over the given interval and comment on how their areas under the curves from 0rad to 2.0rad compare.
(b) Using the data, compute the approximate work done by each torque separately as the cylinder rotates from θ=0rad to θ=2.0rad. Use the trapezoidal rule on each sub-interval defined in the table.
(c) Determine the cylinder’s rotational kinetic energy after it has turned through 2.0rad, assuming it started from rest.
(d) Identify which device (1 or 2) transfers more energy to the cylinder and explain why, referencing both the numerical result and features of the torque-versus-θ profiles.