Physics

Problem

A thin, uniform circular plate of mass

1.5\,\text{kg}

and radius

0.30\,\text{m}

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

0.050\,\text{kg}

lump of clay approaches horizontally and sticks to the rim of the plate at a speed of

3.0\,\text{m/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).

Intuitive explanation

This is a collision problem where momentum isn't conserved—but angular momentum is, because there are no external torques. The key insight is to treat the clay lump and plate as a system, use conservation of angular momentum before and after the collision, and remember that the clay's linear momentum becomes rotational momentum about the plate's center. Calculate the moment of inertia for both objects about the rotation axis, find their angular momenta just before impact, and solve for the final angular velocity when they move together.

Intuitive explanation

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