PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics
Problem
A cyclist accelerates from rest on a straight, level road by exerting a constant angular acceleration of 2.0rad/s2 on the rear wheel for 3.0s. The rear wheel may be approximated as a thin hoop of radius 0.35m that rolls without slipping. Assume the rest of the bicycle and rider have mass 75kg, while the rear wheel has mass 1.0kg. Air resistance and friction in the bearings are negligible during this brief start-up interval.
(a) Decide whether the rear wheel should be treated as a rigid system or as a single object when computing the bicycle’s center-of-mass speed at t=3.0s. Provide a brief justification referring to the type of motion involved.
(b) Determine the linear speed of the bicycle’s center of mass at t=3.0s.
(c) Calculate the translational kinetic energy of the bicycle–rider system at that instant.
(d) If, instead, the analyst had modeled the rear wheel as a single object and ignored its rotation, state whether the speed found in part (b) would be over-estimated, under-estimated, or unchanged. Explain your reasoning without performing additional computations.