A thin, uniform circular plate of mass 1.5kg and radius 0.30m is free to rotate about a fixed axis through its center and perpendicular to the plane of the plate. Initially the plate is at rest. A 0.050kg lump of clay approaches horizontally and sticks to the rim of the plate at a speed of 3.0m/s, moving tangent to the rim just before impact. Treat the lump as a point mass and ignore external torques during the brief collision.
(a) Determine the angular speed of the plate–clay system immediately after the collision.
(b) Calculate the magnitude of the clay’s angular momentum about the plate’s rotation axis just before impact.
(c) Compute the percentage of the clay’s initial kinetic energy that remains as rotational kinetic energy of the system after the collision.
(d) Provide a brief explanation for the energy loss (if any) identified in part (c).