A small ball with mass 1.30 kg is mounted on one end of a rod0.780 m long and of negligible mass.The system rotates in a horizontalcircle about the other end of the rod at 5010 rev/min. (a) Calculatethe rotational inertia of the system about the axis of rotation. (b)There is an air drag of 2.30* 10-2 N on the ball, directed opposite itsmotion.What torque must be applied to the system to keep it rotatingat constant speed?

The flywheel of a steam engine runs with a constant angular velocity of 132 rev/min. When steam is shut off, the friction of the bearings and of the air stops the wheel in 1.40 h. (a) What is the constant angular acceleration, in revolutions per minute-squared, of the wheel during the slowdown? (b) How many revolutions does the wheel make before stopping? (c) At the instant the flywheel is turning at 66.0 rev/min, what is the tangential component of the linear acceleration of a flywheel particle that is 42.7 cm from the axis of rotation? (d) What is the magnitude of the net linear acceleration of the particle in (c)?

With the aid of a string, a gyroscope is accelerated from rest to 40 rad/s in 0.3 s. (a) What is its angular acceleration in rad/s2 ?  (b) How many revolutions does it go through in the process?

A grindstone has a moment of inertia of 6 x 10-3 kg m2. When a constant torque is applied, the flywheel reaches an angular velocity of 1200 rev/min in 15 s. Assuming it started from rest, find the angular acceleration. Find the unbalanced torque applied. Find the angle turned through in the 15 s. Find the work W done on the flywheel by the torque.

Suppose you exert a force of 185N tangential to the outer edge of a grindstone (which is a solid disk) with a radius of 1.56m and a mass of 74kg. What is the angular acceleration of the grindstone αf, in radians per square second, if there is an opposing frictional force of 22.5 N exerted 0.45 m from the axis?

Let’s approximate the motion of a yo-yo with that of a solid cylinder with a string wrapped around it. The string has alength of 1.2 m and the cylinder has a mass of 0.1 kg and a radius of 0.05 m. Suppose the cylinder was released atrest from the top, what would be its velocity when it reaches the bottom?