1. A 3.9 kg stone is tied to a 5.8 m long string and swung around a circle at a constant angular velocity 1.7 1/s. Find the magnitude of the torque about the origin.
2. A uniform meter stick is placed on and parallel to the x axis, with the 50 cm mark at the origin. It is pivoted at the 50 cm mark. A 3.9 N force is applied at the 43 cm mark, and a -4.1 N force is applied at the 90 cm mark. Find the net torque on the rod.
3. A thin disk, mounted on a frictionless vertical shaft of negligible rotational inertia, is rotating at 215 revolutions per minute. An identical disk (that is not initially rotating) is dropped onto the first disk. The frictional force between the disks causes them to rotate at a common angular velocity. Find this common angular velocity.
Use rad/s for your unit.
4. A merry-go-round has a radius of 10 m and a moment of inertia of 663 kg.m2. It is initially spinning with an angular velocity ? = 1.4 rad/s when a 18 kg child crawls from the center to the rim. When the child reaches the rim, what is the angular velocity of the merry-go-round?
Use rad/s for your answer.
5. At the same instant that a 2.7 kg ball is dropped from 30 m above the Earth's surface, a second ball, with a mass of 8.8 kg, is thrown straight upward from the Earth's surface with initial velocity of 1.6 m/s. They move along nearby lines and pass without colliding. At the end of 3 s, what is the height above the Earth of the center of mass of the two-ball system?