Exam 11: Rolling, Torque, and Angular Momentum

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:

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:

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?

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

A man, with his arms at his sides, is spinning on a light frictionless turntable. When he extends his arms:

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 net torque on the stone about the center of the circle is:

Two objects are moving in the x,,y plane as shown. The magnitude of their total angular momentum (about the origin O) is:

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:

When the speed of a rear-drive car is increasing on a horizontal road the direction of the frictional force on the tires is:

An ice skater with rotational inertia I₀ is spinning with angular speed $\omega$ ₀. She pulls her arms in, thereby increasing her angular speed to 4 $\omega$ ₀. Her rotational inertia is then:

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

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:

A 2.0-kg block starts from rest on the positive x axis 3.0 m from the origin and thereafter has an acceleration given by in m/s². The torque, relative to the origin, acting on it at the end of 2.0 s 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 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.

The unit kg.m²/s can be used for:

A wheel rolls without slipping along a horizontal road as shown. The velocity of the center of the wheel is represented by $\rightarrow$ . Point P is painted on the rim of the wheel. The instantaneous velocity of point P is:

A yo-yo, arranged as shown, rests on a frictionless surface. When a force is applied to the string as shown, the yo-yo:

A wheel of radius 0.5 m rolls without sliding on a horizontal surface as shown. Starting from rest, the wheel moves with constant angular acceleration 6 rad/s². The distance in traveled by the center of the wheel from t = 0 to t = 3 s is:

The newton.second is a unit of: