Problem 6: A solid disk of mass M = 4.5 kg and radius R = 0.96 m rotates in the z-y plane as shown. Part (a) What is an expression for the magnitude of the net torque required for the disc to achieve a given rotational speed when starting from rest in terms of M, R, , and t. Part (b) What is an expression for the force that produces this torque if it is applied to the edge of the disc and in a direction that is tangent to the disc in terms of and R? Part (c) If, as soon as the angular speed is = 41 rad/s, the force is immediately removed and a mass m = 0.45 kg is dropped at r = 0.51 m on the disc and sticks there, what would be the new rotational velocity of the disc in rad/s

Problem 7: An ice skater is preparing for a jump with turns and has his arms extended. His moment of inertia is 1.8kgm2 while his arms are extended, and he is spinning at 0.49rev/s. Then he simultaneously pulls his arms in and launches himself into the air at 5.5m/s at an angle of 37 with respect to the ice. His moment of inertia in the air is 0.5kgm Part (a) How long in seconds is the skater in the air? Specify your answer in at least two digits past the decimal point. Part (b) How many revolutions can he execute while airborn? Specify your answer to at least two digits past the decimal point.