A solid uniform cylinder of mass and radius starts from rest at the top of a rough…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A solid uniform cylinder of mass 2.0kg and radius 0.10m starts from rest at the top of a rough inclined plane that makes an angle of 30∘ with the horizontal. The cylinder rolls without slipping down a vertical height of 1.2m before reaching a horizontal surface that is also rough enough to maintain rolling without slipping.
(a) Calculate the speed of the cylinder’s center of mass at the bottom of the incline.
(b) Determine the magnitude of the cylinder’s angular speed about its central axis at that point.
(c) Compute the numerical values of the translational and rotational contributions to the total kinetic energy at the bottom of the incline, and state which form is larger.
(d) Describe, without further calculation, how the answers to parts (a) through (c) would change if the cylinder were replaced by a thin-walled hollow cylinder of the same mass and radius. Provide reasoning for each predicted change.