A wheel of radius 0.20 m is mounted on a frictionless horizontal axis. The rotational inertia of the wheel about the axis is 0.050 kgm2. A massless cord wrapped around the wheel is attached to a 2.0 kg block that slides on a horizontal frictionless surface. If a horizontal force of magnitude P=3.0 N is applied to the block , what is the magnitude of the angular acceleration of the wheel? Assume the cord does not slip on the wheel.

A playground merry-go-round of radius R = 2.00 m has a moment of inertia I = 250 kg · m2 and is rotating at 10.0 rev/min about a frictionless, vertical axle. Facing the axle, a 25.0-kg child hops onto the merry-go-round and manages to sit down on the edge. What is the new angular speed of the merry-go-round?

A cylinder has a cone removed from it.  The cylinder and the conical hole have the same radius (2.06 meters) and height (4.56 meters).  The cylinder has a density of 447 kg/m3. What is the rotational inertia of the cylinder with the cone removed in kg m2?  You can set your origin at the tip of the cone, which is also the center of the base of the cylinder.

In the figure, a wheel of radius 0.234 m is mounted on a frictionless horizontal axis. The rotational inertia of the wheel about the axis is 0.586 kg-m2. A massless cord wrapped around the wheel's circumference is attached to a 4.00 kg box. The system is released from rest.When the box has a kinetic energy of 4.00 J, what are (a) the wheel's rotational kinetic energy and (b) the distance the box has fallen? Assume free-fall acceleration to be equal to 9.81 m/s2. M (a) Number Units (b) Number Units

A uniform spherical shell of mass M = 6.0 kg and radius R = 18.0 cm rotates about a vertical axis on frictionless bearings (see the figure). A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 3.60×10-3 kg m2 and radius r = 6.0 cm, and its attached to a small object of mass m = 4.0 kg. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object after it has fallen a distance h = 1.1 m from rest: Use work - energy considerations

A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a vertical axle through the center of the disk. The platform has a radius of 2.58 m and a rotational inertia of 255 kg·m2 about the axis of rotation. A 53.8 kg student walks slowly from the rim of the platform toward the center. If the angular speed of the system is 2.18 rad/s when the student starts at the rim, what is the angular speed when she is 1.79 m from the center?

A grindstone in the shape of a solid disk (mass M = 50.0 kg) and radius R = 0.200 m (moment of Inertia | = 1/2 MR^2) is rotating at 90.0 rad/s. You press a metal box against the rim with a force F = 180 N and the grindstone comes to rest in 10.0 s. There is a friction force between the grindstone and the box. Find the magnitude of the friction.

A small 0.340-kg object moves on a frictionless horizontal table in a circular path of radius 1.10 m. The angular speed is 7.09 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than 108 N, what is the radius of the smallest possible circle on which the object can move? Number Units

A motor spins a disk (Idisk = 25.5 kg*m2) with a torque of 39 N*m, and a 18 N frictional force acts on the disk at a radius of 1.4 m. Attached to the disk at a radius of 6.6 m is a 13 kg mass. What is the magnitude of the angular acceleration in rad/s2 of the system?

Two wheels A and B in the figure are connected by a belt that does not slip. The radius of B is 4.30 times the radius of A. What would be the ratio of the rotational inertias IA/IB if the two wheels had (a) the same angular momentum and (b) the same rotational kinetic energy? (the absolute tolerance for the answer of a is ± 0.001)(the absolute tolerance for the answer of b is ± 0.0001)