1. A grindstone of radius 4.0 m is initially spinning with an angular speed of 8.0 rad/s. The angular speed is then increased to12 rad/s over the next 4.0 seconds. Suppose that the angular acceleration is constant. during how many revolutions does the grindstone turn through the 4.0-second interval?
2. A wheel of radius 0.5 m rotates with a constant angular speed about an axis perpendicular to its center. A point on the wheel that is 0.2 m from the center has a tangential speed of 2 m/s. Decide the tangential speed of a point 0.3 m from the center of the wheel.
3. On an amusement park ride, passengers are seated in a horizontal circle of radius 7.5 m. The seats begin from rest and are uniformly accelerated for 21 seconds to a maximum rotational speed of 1.4 rad/s. What is the tangential acceleration of the passengers through the first 21 s of the ride?