A turntable of unknown construction is used in a physics lab demonstration. When the turntable is initially at rest, a student gently places a 0.50kg clay disk at a point 0.30m from the center and releases it so that it sticks to the surface without slipping. The student then applies a constant tangential force of 4.0N at the same radial distance for 5.0s. At the end of the push, the turntable–clay system is measured to be rotating at ω=8.0rads−1. Assume the turntable and clay disk together behave as a rigid single object after the clay sticks.
(a) Calculate the work done by the student on the system during the 5.0s interval.
(b) Assuming all of the work goes into rotational kinetic energy, determine the rotational inertia of the combined turntable–clay system about the central axle.
(c) The clay disk alone would have a rotational inertia of 0.045kgm2 about the axle. Using your result from part (b), determine the rotational inertia of the bare turntable.
(d) The instructor claims the turntable is a solid uniform disk. Using your answer to part (c), evaluate this claim by calculating what the radius of such a disk would have to be, given that the turntable’s mass is 4.0kg. State whether the implied radius is reasonable for standard laboratory equipment and explain your reasoning.