A small turntable is rotated by a motor that exerts a torque directly proportional to…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A small turntable is rotated by a motor that exerts a torque directly proportional to the turntable’s angular position according to τ=kθ, where k=3.5N⋅m⋅rad−1. Starting from rest at θ=0, the motor rotates the turntable to θ=0.80rad.
(a) Derive an algebraic expression for the work W performed by the motor as a function of the final angular position θf.
(b) Using your expression from part (a), calculate the numerical value of the work done by the motor in rotating the turntable through 0.80rad. Include appropriate units.