Exam 10: Rotation

A wheel of diameter 3.0 cm has a 4.0 m cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of 2 rad/s². The cord will unwind in:

A force is applied to a billiard ball. In order to calculate the torque created by the force, you also need to know:

String is wrapped around the periphery of a 5.0-cm radius cylinder, free to rotate on its axis. The string is pulled straight out at a constant rate of 10 cm/s and does not slip on the cylinder. As each small segment of string leaves the cylinder, the segment's acceleration changes by:

A car travels north at constant velocity. It goes over a piece of mud which sticks to the tire. The initial acceleration of the mud, as it leaves the ground, is:

Three identical balls are tied by light strings to the same rod and rotate around it, as shown below. Rank the balls according to their rotational inertia, least to greatest.

A particle moves in a circular path of radius 0.10 m with a constant angular speed of 5 rev/s. The acceleration of the particle is:

The angular velocity of a rotating wheel increases 2 rev/s every minute. The angular acceleration of this wheel is:

This graph shows the angular position of an object as a function of time. What is its instantaneous angular velocity at t = 1.5 s?

Two uniform circular disks having the same mass and the same thickness are made from different materials. The disk with the smaller rotational inertia is:

The coordinate of an object is given as a function of time by θ = 7t - 3t², where θ is in radians and t is in seconds. Its angular velocity at t = 3 s is:

A disk with a rotational inertia of 5.0 kg∙m² and a radius of 0.25 m rotates on a fixed axis perpendicular to the disk and through its center. A force of 2.0 N is applied tangentially to the rim. As the disk turns through half a revolution the work done by the force is:

If a wheel turning at a constant rate completes 100 revolutions in 10 s its angular speed is:

An 8.0-cm radius disk with a rotational inertia of 0.12 kg∙m² is free to rotate on a horizontal axis. A string is fastened to the surface of the disk and a 10-kg mass hangs from the other end. The mass is raised by using a crank to apply a 9.0-N.m torque to the disk. The acceleration of the mass is:

A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5)MR². A light string of length 2.5 R is attached to the surface and used to suspend the sphere from the ceiling. Its rotational inertia about the point of attachment at the ceiling is:

The torque exerted on an object can be written as . Here, :

Ten seconds after an electric fan is turned on, the fan rotates at 300 rev/min. Its average angular acceleration is:

A flywheel of diameter 1.2 m has a constant angular acceleration of 5.0 rad/s². The tangential acceleration of a point on its rim is:

A wheel initially has an angular velocity of 18 rad/s but it is slowing at a rate of 2.0 rad/s². By the time it stops it will have turned through:

The figure shows forces acting on a meter stick, which is constrained to rotate around the axis indicated by the dot $\bullet$ Which force(s) create a positive torque around that axis?

A constant torque of 260 N∙m acts on a flywheel. If the flywheel makes 25 complete revolutions, how much work has been done by the torque on the flywheel?