A solid cylinder of mass 2.5 kg and radius 0.20 m rolls without slipping along a…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A solid cylinder of mass 2.5 kg and radius 0.20 m rolls without slipping along a horizontal surface at an initial center-of-mass speed of 3.0 m/s. At time t = 0 a horizontal force of 4.0 N acting opposite to the motion is applied at the cylinder’s axle for a time interval of 1.5 s. Static friction between the cylinder and the surface is sufficient to maintain rolling without slipping at all times, and no other horizontal forces act.
(a) Determine the impulse delivered to the cylinder’s center of mass by the applied force during the 1.5 s interval.
(b) Determine the change in the cylinder’s angular momentum about its central axis due solely to the torque produced by the applied force during the same interval.
(c) Calculate the cylinder’s translational speed immediately after the force ceases.
(d) Verify that the rolling-without-slipping condition is still satisfied at the end of the interval and explain the physical significance of your result.