Exam 11: Rolling, Torque, and Angular Momentum

A thin-walled hollow tube rolls without sliding along the floor. The ratio of its translational kinetic energy to its rotational kinetic energy (about an axis through its center of mass) 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:

A sphere and a cylinder of equal mass and radius are simultaneously released from rest on the same inclined plane sliding down the incline. Then:

A single force acts on a particle P. Rank each of the orientations of the force shown below according to the magnitude of the time rate of change of the particle's angular momentum about the point O, least to greatest.

The fundamental dimensions of angular momentum are:

Two wheels roll side-by-side without sliding, at the same speed. The radius of wheel 2 is twice the radius of wheel 1. The angular velocity of wheel 2 is:

When a man on a frictionless rotating stool extends his arms horizontally, his rotational kinetic energy:

A hoop, a uniform disk, and a uniform sphere, all with the same mass and outer radius, start with the same speed and roll without sliding up identical inclines. Rank the objects according to how high they go, least to greatest.

A single force acts on a particle situated on the positive x axis. The torque about the origin is in the negative z direction. The force might be:

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 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:

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:

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, a distance of 0.75 m from the origin. The z component of the angular momentum around the origin is:

A uniform disk has radius R and mass M. When it is spinning with angular velocity $\omega$ about an axis through its center and perpendicular to its face its angular momentum is $\omega$ . When it is spinning with the same angle velocity about a parallel axis a distance h away its angular momentum is: