Exam 10: Rotational Kinematics and Energy

A child is riding a merry-go-round which completes one revolution every 8.36 s. The child is standing 4.65 m from the center of the merry-go-round. What is the tangential speed of the child?

A car with tires whose radius is 35 cm is traveling along a highway at 29.8 m/s. What is the angular speed of the tires?

When a rigid body rotates about a fixed axis all the points in the body have the same linear displacement.

FIGURE 10-2 -Figure 10-2 illustrates a simplified roller bearing. The outer hollow cylinder has a radius of 1.20 cm and is stationary. The inner cylinder has a radius of 1.00 cm and is rotating at 12.0 rpm. Between the two cylinders are several small cylinders with a radius of 0.100 cm, which roll without slipping on both the inner and outer cylinders. Only one of these cylinders is shown in the figure. How long does it take a small cylinder to complete a full revolution around the inner cylinder?

A child is riding a tricycle. The pedals are attached directly to the front wheel, which has a radius of 13 cm. The rear wheels are smaller, and have a radius of 8.0 cm. If the child is pedaling at 16 rpm, what is the angular speed of the rear wheels?

A boy and a girl are riding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

A solid disk is released from rest and rolls without slipping down an inclined plane that makes an angle of 25.0° with the horizontal. What is the speed of the disk after it has rolled 3.00 m, measured along the plane?

A child is riding a merry-go-round which completes one revolution every 8.36 s. The child is standing 4.65 m from the center of the merry-go-round. (a) What is the tangential speed of the child? (b) What is the magnitude of the centripetal acceleration of the child?

A grinding wheel is spinning at a rate of 20.0 revolutions per second. When the power to the grinder is turned off, the grinding wheel slows with constant angular acceleration and takes 80.0 s to come to a rest. (a) What was the angular acceleration of the grinding wheel as it came to rest? (b) How many rotations did the wheel make during the time it was coming to rest?

A solid sphere is rolling without slipping along a horizontal surface with a speed of 5.50 m/s when it starts up a ramp that makes an angle of 25.0° with the horizontal. What is the speed of the sphere after it has rolled 3.00 m up the ramp?

A child is riding a merry-go-round which completes one revolution every 8.36 s. The child is standing 4.65 m from the center of the merry-go-round. What is the magnitude of the centripetal acceleration of the child?

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

A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii. If the three are released simultaneously at the top of an inclined plane, which will reach the bottom first?

The diameter of the Moon is 3.78 × 10⁶ m. It subtends an angle of 0.00982 radians at the surface of Earth. How far is the Moon from Earth?

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

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger centripetal acceleration?

A wheel rotates through an angle of 13.8 rad as it slows down from 22.0 rad/s to 13.5 rad/s. What is the magnitude of the average angular acceleration of the wheel?

A 2.00-kg solid sphere of radius 5.00 cm rolls down a 20.0° inclined plane starting from rest. (a) What is the magnitude of the acceleration of the center of mass of the sphere? (b) How far down the plane does it roll without slipping in 1.00 s?

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

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