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AP Physics C: Mechanics
6.4 Conservation of Angular Momentum
6.1 Rotational Kinetic Energy
5.4 Rotational Inertia
Multi-Unit
AdvancedMCQMathematicalProportional Analysis25.4k
A physical setup diagram shown in perspective view. A horizontal circular disk of radius \(R\) is mounted on a vertical axle passing perpendicularly through its center. The axle is represented by a vertical line extending both above and below the center of the disk. A curved counterclockwise arrow near the axle indicates rotation with angular speed \(\omega_0\). A dashed radial horizontal line segment extends from the center of the disk's top face to a point at distance \(r\) from the axle, labeled \(r\). Directly above this point at distance \(r\), a small spherical lump of clay of mass \(m\) is shown with a downward straight arrow indicating it is falling vertically toward the disk. The radius of the disk is indicated by a dimension line along the top surface from the center to the outer rim labeled \(R\). No other labels, lines, text, or axes appear.
A lump of clay of mass \(m\) dropped vertically onto a rotating disk of mass \(M\) and radius \(R\).
A uniform solid disk of mass \(M\) and radius \(R\) rotates horizontally about a frictionless, fixed vertical axle through its center with initial angular speed \(\omega_0\).

A small lump of clay of mass \(m\) is dropped vertically from a negligible height onto the disk and sticks to its surface at a radial distance \(r\) from the axle.

Which of the following expressions represents the fraction of the initial kinetic energy of the disk that is converted into thermal energy during the collision?

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