13. Rotational Inertia & Energy

A 150-g baseball, 3.85 cm in radius, leaves the pitcher's hand with 30 m/s horizontal and 20 rad/s clockwise. Calculate the ball's linear, rotational, and total kinetic energy.

A hollow sphere of mass M and radius R rolls without slipping on a horizontal surface with angular speed W. Calculate the ratio of its linear kinetic energy to its total kinetic energy.

An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 117 kg. When the airplane's engine is first started, it applies a constant torque of 1950 Nm to the propeller, which starts from rest. What is the instantaneous power output of the motor at the instant that the propeller has turned through 5.00 revolutions?

Compute the torque developed by an industrial motor whose output is 150 kW at an angular speed of 4000 rev/min.

An electric motor consumes 9.00 kJ of electrical energy in 1.00 min. If one-third of this energy goes into heat and other forms of internal energy of the motor, with the rest going to the motor output, how much torque will this engine develop if you run it at 2500 rpm?

A 2.80-kg grinding wheel is in the form of a solid cylinder of radius 0.100 m. What constant torque will bring it from rest to an angular speed of 1200 rev/min in 2.5 s?

A hoop of mass $m$ and radius $R$ rolls without slipping down a hill of height $5.75$ m. What is the speed of the hoop's center of mass at the bottom of the hill?