Name: ___________________ Period: _____ AP-C 10 Problems f or Review: Rotation and Moment of Inertia (#1) A solid disk of mass 0 .11 kg & radius 0.53 m st arts at rest and is given a c onstant torque of 0.023 N*m for 5.0 sec. (a) Calculate the moment of inertia o f the disk. (b) Calculate the angul ar acceleration o f the disk. (c) Through what angle (in radia ns) will the disk rotate in 5 seconds? (d) How many complete rotat ions does your answer to (b) represent? (e) What is the final angular velocity of the disk? (f) Convert your answer from (e) into RPM’s (rotations per minute): (g) If this disk were a pen dulum that swung around an axis loca ted at the edge, find the period T. (#2) A hoop of mass 0.74 kg and radius 0.43 m is at the top of a 2.0 m high inclined plane. It starts at rest, and then rolls without slipping down to the bottom. (a) Calculate the moment of inertia o f the hoop. (b) Using conservation of energy, find t he hoop’s angular velocity at the bottom of the incline. (c) If this hoop were a pendulum tha t swung around an axis locat ed at the edge, find t he period T. (#3) A bowling ball , which can be assumed to b e a solid sphere, has a mass o f 7.1 kg and a radius of 0.24 m. (a) Calculate the moment of inertia o f the ball. (b) If the ball is given 6.2 J of KE, and it rolls without slipping, then what is its velocity? (c) If this ball were a p endulum that swung around an axis loc ated at the edge, fi nd the period T. (#4) The Earth turns at a ra te of onc e every 24 hours. The Earth’s ma ss is 6 x 10 24 kg, and its radius is 6.37 x 10 6 meters. (a) If the rotation were to be decelerated at a ra te of 1 radian/year 2 , how many years would pass by before the Earth had stopped spinning? (b) Calculate the force (applied at the equator and against the Earth’s direction of rotation) which would be needed to make this deceleration happen. (#5) A solid disk of mass 1.5 kg and radius 0.5 m starts at rest. A string is wrapped around it and is pulled with a constant force of 2.0 N for 3.0 seconds. (a) Calculate the angul ar acceleration o f the disk. (b) Through what angle (in radia ns) will the disk rotate in 3 seconds? (c) How many complet e rotations does your answer to ( b) represent? (d) What is the final angular veloc ity of the disk? (e) Convert your answer to (d) into RPM’s (rotations per minute). (#6) Hollow sphere!