Exam 10: Rotational Kinematics and Energy

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 linear displacement?

A spool whose inner core has a radius of 1.00 cm and whose end caps have a radius of 1.50 cm has a string tightly wound around the inner core. The spool is free to roll without slipping on a horizontal surface. If the string unwinds horizontally from the top of the core with a constant speed of 29.0 cm/s, what is the speed of the spool?

Earth's radius is 6.38 × 10⁶ m, and it completes one revolution every day. What is the magnitude of the centripetal acceleration 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 displacement.

A fan is turned off, and its angular speed decreases from 10.0 rad/s to 6.3 rad/s in 5.0 s. What is the magnitude of the angular acceleration of the fan?

Express an angle of 35.20 rad in degrees.

A wheel of radius R is rolling on a horizontal surface. Its center is moving forward with speed v. A point on the wheel a distance r/3 below the center is moving forward at a speed 2v/3. The wheel is

FIGURE 10-2 -Figure 10-2 illustrates a simplified roller bearing. The inner cylinder has a radius of 1.0 cm and is stationary. The outer hollow cylinder has a radius of 1.2 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 pencil, 15.7 cm long, is released from a vertical position with the eraser end resting on a table. The eraser does not slip. Treat the pencil like a uniform rod. What is the angular speed of the pencil just before it hits the table?

A car is moving in a circular path. At a certain instant, it has zero tangential acceleration and a non-zero centripetal acceleration. What is the car doing at that instant?

A solid cylinder with a radius of 10 cm and a mass of 3.0 kg is rotating about its center with an angular speed of 3.5 rad/s. What is its kinetic energy?

A massless rod of length 1.00 m has a 2.00-kg mass attached to one end and a 3.00-kg mass attached to the other. The system rotates about a fixed axis perpendicular to the rod that passes through the rod 30.0 cm from the end with the 3.00-kg mass attached. The kinetic energy of the system is 100 J. (a) What is the moment of inertia of this system about this axis? (b) What is the angular speed of this system?

Consider a hoop of radius R and mass M rolling without slipping. Which form of kinetic energy is larger, translational or rotational?

A Ferris wheel with a radius of 14.0 m rotates at a constant rate, completing one revolution in 30.0 s. What is the apparent weight of a 60.0-kg passenger when she is at the bottom of the wheel?

An object is moving in a circular path with an angular speed of 1.52 rad/s. How long does it take the object to complete one revolution?

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 tangential speed?

How long does it take for a rotating object to speed up from 15.0 to 33.3 rad/s if it has an angular acceleration of 3.45 rad/s²?

A string is wrapped tightly around a fixed pulley that has a moment of inertia of 0.0352 kg m² and a radius of 12.5 cm. The string is pulled away from the pulley with a constant force of 5.00 N. As the string unwinds the pulley begins to rotate. What is the speed of the string after it has unwound 1.25 m?

A 10-m plank with a mass of 80 kg is being moved by rolling it over two cylindrical logs, each with a mass of 10 kg and a radius of 20 cm, placed 2 m from either end of the plank. As the plank is pushed, the logs roll on the ground without slipping, and the plank does not slip on the rollers. A force of 250 N is applied to the plank. What is the speed of the plank after it has moved 2 m, starting from rest?

The Sun subtends an angle of 0.00928 radians at the surface of the earth. Its distance from Earth is 1.50 x 10¹¹ m. What is the diameter of the Sun?