A solid uniform disk of mass and radius is mounted on a frictionless axle through its…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A solid uniform disk of mass M and radius R is mounted on a frictionless axle through its center so that it can rotate freely in a horizontal plane. A small block of mass m approaches the disk along a straight line that is tangent to the rim, moving with speed v. The block sticks to the rim at the instant of contact. Treat the block as a point mass.
(a) Determine the magnitude of the block’s angular momentum about the center of the disk just before impact.
(b) Determine the angular speed ω of the disk–block system immediately after the collision.
(c) Compute the ratio of the system’s kinetic energy immediately after the collision to the block’s initial kinetic energy.
(d) Suppose the solid disk is replaced with a thin hoop of the same mass M and radius R. Without further calculation, state whether the angular speed immediately after the collision would be less than, greater than, or the same as in part (b), and justify your choice.