Discussion
A disk of mass \(m = 0.25\) g and radius \(r = 10\) mm is at rest relative to a mass-less horizontal turntable spinning about a vertical axis at an angular speed of \(\omega = 2\) rad/s. The turntable is assumed to be mounted on frictionless bearings. Another identical, initially non-rotating disk is dropped onto the spinning disk. Friction causes both disks (and the turntable) to eventually rotate at the same angular speed. The eventual angular speed of the disks is
Answer: B
The final angular speed is 1 rad/s.
The turntable is massless and its bearings are frictionless, so no external torque acts about the axis and angular momentum is conserved. Friction between the disks is internal.
\[ \begin{aligned} I\omega_{0} &= (I + I)\omega_{f} \\ \omega_{f} &= \frac{\omega_{0}}{2} = \frac{2}{2} = 1\ \text{rad/s} \end{aligned} \]
The mass and radius are not needed, since both disks are identical and their moments of inertia cancel. 2 rad/s would mean the second disk added no inertia, 4 rad/s would violate conservation, and 0.15 rad/s has no basis. Kinetic energy is not conserved: half of it is lost to friction.
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