Exam 10: Rotation

A disk with a rotational inertia of 5.0 kg .m² and a radius of 0.25 m rotates on a frictionless fixed axis perpendicular to the disk and through its center. A force of 8.0 N is applied along the rotation axis. The angular acceleration of the disk is:

A circular saw is powered by a motor. When the saw is used to cut wood, the wood exerts a torque of 0.80 N · m on the saw blade. If the blade rotates with a constant angular velocity of 20 rad/s the work done on the blade by the motor in 1.0 min is:

To increase the rotational inertia of a solid disk about its axis without changing its mass:

The meter stick shown below rotates about an axis through the point marked $\bullet$ , 20 cm from one end. Five forces act on the stick: one at each end, one at the pivot point, and two 40 cm from one end, as shown. The magnitudes of the forces are all the same. Rank the forces according to the magnitudes of the torques they produce about the pivot point, least to greatest.

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

Four identical particles, each with mass m, are arranged in the x, y plane as shown. They are connected by light sticks to form a rigid body. If m = 2.0 kg and a = 1.0 m, the rotational inertia of this array about the y-axis is:

Consider four objects, each having the same mass and the same radius: 1. a solid sphere 2. a hollow sphere 3. a flat disk in the x,y plane 4. a hoop in the x,y plane The order of increasing rotational inertia about an axis through the center of mass and parallel to the z axis is:

$\tau$ = I $\alpha$ for an object rotating about a fixed axis, where $\tau$ is the net torque acting on it, I is its rotational inertia, and $\alpha$ is its angular acceleration. This expression:

The angular velocity vector of a spinning body points out of the page. If the angular acceleration vector points into the page then:

A wheel initially has an angular velocity of 18 rad/s. It has a constant angular acceleration of 2.0 rad/s² and is slowing at first. What time elapses before its angular velocity is18 rad/s in the direction opposite to its initial angular velocity?

The angular speed of the second hand of a watch is:

A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center. Assume the hoop is connected to the rotation axis by light spokes. With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown. Rank the objects according the their angular velocities after a given time t, least to greatest.

The angular velocity of a rotating wheel increases 2 rev/s every minute. The angular acceleration, in rad/s² of this wheel is:

For a wheel spinning on an axis through its center, the ratio of the radial acceleration of a point on the rim to the radial acceleration of a point halfway between the center and the rim 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:

For a wheel spinning on an axis through its center, the ratio of the tangential acceleration of a point on the rim to the tangential acceleration of a point halfway between the center and the rim is:

A block is attached to each end of a rope that passes over a pulley suspended from the ceiling. The blocks do not have the same mass. If the rope does not slip on the pulley, then at any instant after the blocks start moving, the rope:

A and B are two solid cylinders made of aluminum. Their dimensions are shown. The ratio of the rotational inertia of B to that of A about the common axis X─X' is:

A wheel starts from rest and spins with a constant angular acceleration. As time goes on the acceleration vector for a point on the rim:

A uniform solid cylinder made of lead has the same mass and the same length as a uniform solid cylinder made of wood. The rotational inertia of the lead cylinder compared to the wooden one is: