(Solved): Please show work Loarning Goal: To understand how to use conservation of angular momentum to solve p ...

Loarning Goal: To understand how to use conservation of angular momentum to solve problems involving collisions of rotating bodies. Consider a fumtable to be a circular disk of moment of inertia \( I_{t} \) rotating at a constant angular velocity \( \omega_{1} \) around an axis through the center and perpendicular to the plane of the disk (the disk's "primary axis of symmetry"). The axis of the disk is vertical and the disk is supported by frictionless bearings. The motor of the turntable is off, so there is no axternal torque being applied to the axis. Another disk (a record) is dropped onto the first such that it lands coaxially (the axes coincide). The moment of inertia of the record is \( I_{\mathrm{t}} \). The initial angular velocity of the second disk is zero. There is frictign botween the fwo disks. After this "rotational collision," the dieks will eventually rotate with the same anyular volocity. Assume that the turntable deccelerated during time \( \Delta t \) betore reaching the final angular velocity \( (\Delta t \) is the time interval between the moment when the top disk is dropped and the time that the disks begin to spin at the same angular velocity). What was the average torque, \( (\tau\rangle \), acting on the bottom disk due to friction with the record? Express the torque in terms of \( I_{\mathrm{I}}, \omega_{\mathrm{i}}, \omega_{\mathrm{I}} \), and \( \Delta t \).