A track is mounted on a large wheel that is free to turn with negligible friction about a vertical axis (the figure). A toy train of mass m is placed on the track and, with the system initially at rest, the train's electrical power is turned on. The train reaches a steady speed of 0.181 m/s with respect to the track. What is the angular speed of the wheel if its mass is 1.87m and s radius is 0.603 m? (Treat the wheel as a hoop, and neglect the mass of the spokes and hub.)

In the figure here, a cylinder having a mass of 2.0 kg can rotate about its central axis through point O. Forces are applied as shown: F₁ = 4.8 N, F₂ = 4.9 N, F3 = 9.9 N, and F4 = 1.9 N. Also, r = 2.4 cm and R = 18 cm. Taking the clockwise direction to be negative, find the angular acceleration of the cylinder. (During the rotation, the forces maintain their same angles relative to the cylinder.) Number i -9.1 F₁ Rotation axis Unit rad/s^2 R 0 14

A star, spinning at a rate of 2.00 rev/s, runs out of thermonuclear fuel and suddenly contracts to 1/35 of its original radius. What is its new rate of rotation?

A 250 g , 25-cm diameter plastic disk is spun on an axle through its center by an electric motor. What torque must the motor supply to take the disk from 0 to 1900 rpm in 4.7 s ? Express your answer in newton-meters.

A 7.2-kg ball is tied to the end of a string.  The ball is then swung at a constant angular velocity of 14 rad/s in a horizontal circle of radius 2.2 m.  What is the torque on the stone?

A grinder consists of a 5.34 kg steel block on a 1.87 m long arm that spins around a table. If the angular acceleration is -1.02 rads/s2, what is the coefficient of friction between the steel block and the table?

A top-loading washing machine has a cylindrical basket that rotates about a vertical axis. The basket of one such machine starts from rest and reaches an angular speed of 7.0 rev/s in 10.0 s. The lid of the machine is then opened, which turns off the machine, and the basket slows to rest in 9.0 s. Through how many revolutions does the basket turn during this 19 s interval? Assume constant angular acceleration while it is starting and stopping.

A 1.80 kg toy race car is slowing down while travelling around a circular horizontal track. If the track has a diameter of 1.51 m and the coefficient of rolling friction between the track and the race car is 0.260, what is the magnitude of angular acceleration?

A small block with a mass of 0.0600 kg is attached to a cord passing through a hole in a frictionless, horizontal surface (Figure 1). The block is originally revolving at a distance of 0.37 mm from the hole with a speed of 0.79 m/sm/s. The cord is then pulled from below, shortening the radius of the circle in which the block revolves to 0.13 mm. At this new distance, the speed of the block is 2.25 m/s.    What is the tension in the cord in the original situation when the block has speed v0 = 0.79 m/sm/s? What is the tension in the cord in the final situation when the block has speed v1 = 2.25 m/s? How much work was done by the person who pulled on the cord?

A 1.2-kg ball is tied to the end of a string. The ball is then swung at a constant angular velocity of 9 rad/s in a horizontal circle of radius 2.1 m. What is the torque on the stone?