Exam 11: Rolling, Torque, and Angular Momentum

A pulley with radius R is free to rotate on a horizontal fixed axis through its center. A string passes over the pulley. Mass m₁ is attached to one end and mass m₂ is attached to the other. The portion of the string attached to m₁ has tension T₁ and the portion attached to m₂ has tension T₂. The magnitude of the total external torque, about the pulley center, acting on the masses and pulley, considered as a system, is given by:

The newton.second is a unit of:

When a woman on a frictionless rotating turntable extends her arms out horizontally, her angular momentum:

A 2.0-kg block travels around a 0.50-m radius circle with an angular velocity of 12 rad/s. The magnitude of its angular momentum about the center of the circle is:

A 2.0-kg stone is tied to a 0.50 m long string and swung around a circle at a constant angular velocity of 12 rad/s. The circle is parallel to the xy plane and is centered on the z axis, 0.75 m from the origin. The magnitude of the torque about the origin is:

A forward force acting on the axle accelerates a rolling wheel on a horizontal surface. If the wheel does not slide the frictional force of the surface on the wheel is:

A hoop rolls with constant velocity and without sliding along level ground. Its ratation kinetic energy is:

A phonograph record is dropped onto a freely spinning turntable. Then:

A 5.0-kg ball rolls without sliding from rest down an inclined plane. A 4.0-kg block, mounted on roller bearings totaling 100 g, rolls from rest down the same plane. At the bottom, the block has:

Two uniform cylinders have different masses and different rotational inertias. They simultaneously start from rest at the top of an inclined plane and roll without sliding down the plane. The cylinder that gets to the bottom first is:

Possible units of angular momentum are:

When we apply the energy conversation principle to a cylinder rolling down an incline without sliding, we exclude the work done by friction because:

Two pendulum bobs of unequal mass are suspended from the same fixed point by strings of equal length. The lighter bob is drawn aside and then released so that it collides with the other bob on reaching the vertical position. The collision is elastic. What quantities are conserved in the collision?

Two disks are mounted on low-friction bearings on a common shaft. The first disc has rotational inertia I and is spinning with angular velocity $\omega$ . The second disc has rotational inertia 2I and is spinning in the same direction as the first disc with angular velocity 2 $\omega$ as shown. The two disks are slowly forced toward each other along the shaft until they couple and have a final common angular velocity of:

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 to their angular momenta after a given time t, least to greatest.

A rod rests on frictionless ice. Forces that are equal in magnitude and opposite in direction are simultaneously applied to its ends as shown. The quantity that vanishes is its:

A pulley with radius R and rotational inertia I is free to rotate on a horizontal fixed axis through its center. A string passes over the pulley. A block of mass m₁ is attached to one end and a block of mass m_2, is attached to the other. At one time the block with mass m₁ is moving downward with speed v. If the string does not slip on the pulley, the magnitude of the total angular momentum, about the pulley center, of the blocks and pulley, considered as a system, is given by:

Two identical disks, with rotational inertia I (= 1/2 MR²), roll without slipping across a horizontal floor and then up inclines. Disk A rolls up its incline without sliding. On the other hand, disk B rolls up a frictionless incline. Otherwise the inclines are identical. Disk A reaches a height 12 cm above the floor before rolling down again. Disk B reaches a height above the floor of:

As a 2.0-kg block travels around a 0.50-m radius circle with an angular speed of 12 rad/s. The circle is parallel to the xy plane and is centered on the z axis, 0.75 m from the origin. The component in the xy plane of the angular momentum around the origin has magnitude:

A uniform sphere of radius R rotates about a diameter with angular momentum of magnitude L. Under the action of internal forces the sphere collapses to a uniform sphere of radius R/2. The magnitude of its new angular momentum is: