The rotational speed of a shaft powered by an electric motor is controlled such that it cannot exceed 450 rev/min. A switching mechanism disconnects power once the shaft hits 450 rev/min. Suppose the shaft has a mass of 36.0 kg and a diameter of 420 mm and power is disconnected at t = 0. The shaft slows down as it delivers power to a load. If it makes 140 revolutions before power is reconnected at t = 23.0 s, what is the rotational speed in RPM at the moment the power is reconnected?

A rotary dining table top lies in the xy plane and rotates about its central axis that is parallel to the z-axis.  At t = 0, the angular velocity of the top, ω_z = -5.00 rad/s. At t = 5.50 s, the angular velocity has increased steadily to +8.50 rad/s. Taking counterclockwise rotation as positive, determine the angular displacement of the disk at t = 5.50 s. 

A disk lies in the xy plane and rotates about its central axis that is parallel to the z-axis.  At t = 0, the angular velocity of the disk, ω_z = -4.80 rad/s. At t = 7.00 s, the angular velocity has increased steadily to +8.90 rad/s. Taking counterclockwise rotation as positive, determine magnitude and state whether the angular acceleration is positive or negative during this time. 

A grinding wheel of radius 8.0 cm rotates clockwise at a constant speed of 650 rpm. Due to a power outage, the wheel completely stops turning in 12s. Calculate the number of revolutions that the wheel makes before stopping.    

A 1.0 kg solid cylinder with a radius of 15 cm is rotating at an angular speed of 230 rpm about its central frictionless axis. You want to stop the cylinder in 30 s by applying a friction force f to the outer edge. Determine the magnitude of f.

What is the angular acceleration of the forearm when it propels a 1.50-kg apple from rest to 8.6 m/s in 0.39 s, solely through elbow rotation driven by the triceps muscle?

What is the final angular speed in rpm of a space simulator, which initially starts from rest and completes 24 rotations in 1.2 minutes, aimed at training astronauts for spacecraft maneuvering?