Two concentric, frictionless turntables share the same vertical axis in a physics laboratory. Disk A (inner) has moment of inertia IA=0.40kgm2 and Disk B (outer) has moment of inertia IB=0.60kgm2. A compact internal motor connecting the disks can exert a constant torque of magnitude τm on Disk A for a short time interval Δt, simultaneously exerting an equal‐magnitude opposite torque on Disk B.
Initially, both disks are at rest and no external torques act on the system.
(a) Derive an expression for the angular momentum of Disk A at the end of the time interval Δt in terms of τm, Δt, and IA.
(b) Derive an expression for the angular speed of Disk B at the same instant.
(c) Show algebraically that the total angular momentum of the two‐disk system remains zero throughout the process, and explain the physical significance of this result.
(d) Suppose τm=1.5Nm and Δt=2.0s. Calculate the numerical angular speeds of both disks at the end of the interval.
(e) After the motor shuts off, a thin ring of clay is gently dropped onto Disk A, sticking to its rim and doubling IA while exerting negligible external torque. Determine the new angular speed of Disk A immediately after the clay sticks, and state how (if at all) this affects Disk B.