A gymnast stands on a frictionless turntable that can rotate about a vertical axis. The combined moment of inertia of the gymnast and turntable is 2.8 kg·m². Initially, the system is at rest. A horizontal external force of 15 N is applied tangentially at the edge of the 0.60 m-radius turntable by briefly pressing a broom handle against its rim for 0.50 s. The force always points in the same direction as the rim moves under the broom (so the force remains tangent throughout the contact).
(a) Compute the magnitude and direction of the torque acting on the system while the force is applied.
(b) Determine the angular acceleration of the system during the 0.50 s interval.
(c) Calculate the angular velocity acquired by the system at the end of the interval.
(d) After the broom loses contact, a small but non-negligible frictional torque of magnitude 0.20 N·m opposite the rotation acts on the turntable. Qualitatively describe how the angular velocity will change over time. Will the system ever reverse its direction of rotation? Justify your answer based on the sign of the net torque after contact ends.