Exam 11: Rolling, Torque, and Angular Momentum

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 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 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. At the end of 2.0 s its angular momentum about the origin is:

Which of the following is a vector quantity?

Possible units of angular momentum are:

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 I $\omega$ . When it is spinning with the same angle velocity about a parallel axis a distance h away its angular momentum is:

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

A hoop (I = MR²) of mass 2.0 kg and radius 0.50 m is rolling at a center-of-mass speed of 15 m/s. An external force does 750 J of work on the hoop. What is the new speed of the center of mass of the hoop?

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:

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:

When a wheel rolls without slipping,

The fundamental dimensions of angular momentum are:

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:

Which of the following is NOT a vector?

A block with mass M, on the end of a string, moves in a circle on a horizontal frictionless table as shown. As the string is slowly pulled through a small hole in the table:

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:

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 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, 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.