A uniform disk of mass 0.80 kg and radius 0.15 m is spun up to an angular speed of 20…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A uniform disk of mass 0.80 kg and radius 0.15 m is spun up to an angular speed of 20 rad/s while held just above a horizontal floor. The disk is then gently lowered so that it makes contact with the floor but is not given any initial horizontal push. The coefficient of kinetic friction between the disk and the floor is 0.30.
Respond to the prompts below. Unless explicitly requested, answers may be expressed symbolically.
(a) Immediately after contact, in which horizontal direction does the frictional force on the disk act at the point of contact? Explain using the motion of the surface of the disk relative to the floor.
(b) Describe qualitatively how the center-of-mass linear momentum of the disk changes from the instant of contact until pure rolling begins.
(c) Derive an expression for the final center-of-mass speed vf of the disk at the instant pure rolling first occurs in terms of its initial angular speed ω0 and its radius R.
(d) Compare the rotational kinetic energy of the disk just before contact with its rotational kinetic energy once pure rolling is established. Explain any difference.
(e) For the entire slipping interval, state whether the net work done by friction on the disk is positive, negative, or zero. Justify your answer with energy considerations.