A thin-walled cylindrical shell (hoop) of mass and radius is spun up while its center…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A thin-walled cylindrical shell (hoop) of mass 0.80kg and radius 0.15m is spun up while its center is held fixed above a horizontal surface. When the shell reaches an angular speed of 22rads−1 (counterclockwise as viewed from above), it is gently lowered until it just contacts the surface; at that instant the center of mass is still at rest relative to the surface. The coefficient of kinetic friction between the shell and the surface is 0.20, and air resistance is negligible.
(a) While the shell is slipping, derive an expression for the horizontal acceleration of its center of mass in terms of known quantities and constants.
(b) Determine the time required for the shell to transition from slipping to rolling without slipping.
(c) Calculate the linear speed of the center of mass once pure rolling is achieved.
(d) Determine the fraction of the shell’s initial kinetic energy that remains as mechanical (translational plus rotational) energy after pure rolling begins.