Exam 10: Rotational Kinematics and Energy

FIGURE 10-2 -Figure 10-2 illustrates a simplified roller bearing. The outer hollow cylinder has a radius of 1.2 cm and is stationary. The inner cylinder has a radius of 1.0 cm and is rotating at 10 rpm. Between the two cylinders are several small cylinders with a radius of 0.10 cm, which roll without slipping on both the inner and outer cylinders. Only one of these cylinders is shown in the figure. What is the angular speed of the small cylinders?

A wheel rotates through an angle of 320° as it slows down from 78.0 rpm to 22.8 rpm. What is the magnitude of the average angular acceleration of the wheel?

When a rigid body rotates about a fixed axis all the points in the body have the same angular acceleration.

A solid sphere and a solid cylinder of the same mass and radius roll without slipping at the same speed. It is correct to say that the total kinetic energy of the solid sphere is

In a part of a printing press, a roller with a radius of 10 cm, rolls without slipping on the outside of a fixed cylinder with a radius of 30 cm. There is a connecting rod that connects the center of the cylinder to the axle of the roller. If the angular speed of the roller is 60 rad/s, what is the angular speed of the connecting rod?

Earth's radius is 6.38 × 10⁶ m, and it completes one revolution every day. What is the tangential speed of a person standing on the equator?

When a rigid body rotates about a fixed axis all the points in the body have the same angular speed.

Rolling without slipping depends on static friction between the rolling object and the ground.

A string is wrapped tightly around a fixed pulley that has a moment of inertia of 0.0352 kg and a radius of 12.5 cm. A mass of 423 g is attached to the free end of the string. With the string vertical and taut, the mass is released so it can descend under the influence of gravity. As the mass descends, the string unwinds and causes the pulley to rotate. What is the speed of the mass after it has fallen through 1.25 m?

Express an angular speed of 33.3 rpm in rad/s.

A dumbbell-shaped object is composed by two equal masses, m, connected by a rod of negligible mass and length r. If I₁ is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and I₂ is the moment of inertia with respect to an axis passing through one of the masses we can say that

Suppose a solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

What is the quantity used to measure an object's resistance to changes in rotational motion?

A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane. Which object reaches the bottom of the incline first?

A potter's wheel is rotating at 1.00 rpm. What centripetal force is required to hold a 1.00 g lump of clay in place, 10.0 cm from the axis of rotation?

Two children ride on a merry-go-round, George is at a greater distance from the axis of rotation than Jacques. It is a true statement that

A compact disk rotates at 210 revolutions per minute. What is its angular speed in rad/s?

In a bicycle, the pedals drive the chainwheel, which is connected by means of a chain to the cogwheel, a small wheel attached to the rear wheel. In a certain bicycle, the radius of the chainwheel is 12.0 cm, the radius of the cogwheel is 4.0 cm, and the radius of the rear wheel is 66.0 cm. At what rate should the cyclist be pedaling in order for the bicycle to have a forward speed of 10.0 m/s?

The moment of inertia of a uniform rod (about its center) is given by I = ML²/12. What is the kinetic energy of a 120-cm rod with a mass of 450 g rotating about its center at 3.60 rad/s?

A bicycle whose wheels have a radius of 66 cm is traveling at 2.0 m/s. If the wheels do not slip, what is the angular speed of the wheels?