A uniform solid disk of mass and radius rests on a low-friction horizontal surface…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A uniform solid disk of mass 2.0kg and radius 0.30m rests on a low-friction horizontal surface and is free to rotate about its central vertical axis. A 0.50kg lump of soft clay slides across the surface at 4.0ms−1 on a straight line that is tangent to the rim of the disk and sticks to the rim upon contact. Ignore any horizontal external forces other than the brief normal and friction forces between the clay and disk during sticking.
Treat the Earth as an external body throughout.
(a) Derive an algebraic expression for the final angular speed ωf of the disk–clay system immediately after the clay sticks, in terms of the given masses, radius, and incoming clay speed.
(b) Calculate the numerical value of ωf for the given data.
(c) The same lump of clay is now projected so that its line of motion passes directly through the disk’s center before sticking. Qualitatively describe how the final angular speed would compare with the value found in part (b), and justify your answer in terms of angular momentum and torque considerations.