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Exam 9: Rotational Dynamics

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Question 21

Multiple Choice

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A 2.0-kg solid cylinder of radius 0.5 m rotates at a rate of 40 rad/s about its cylindrical axis. What power is required to bring the cylinder to rest in 10 s?

A) 20 W
B) 40 W
C) 160 W
D) 200 W
E) 400 W

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Question 22

Multiple Choice

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A hollow cylinder of mass M and radius R rolls down an inclined plane. A block of mass M easily slides down an identical inclined plane. Complete the following statement: If both objects are released at the same time from the top of their inclined planes,

A) the cylinder will reach the bottom first.
B) the block will reach the bottom first.
C) the block will reach the bottom with the greater kinetic energy.
D) the cylinder will reach the bottom with the greater kinetic energy.
E) both the block and the cylinder will reach the bottom at the same time.

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Question 23

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A 3.0-kg ball and a 1.0-kg ball are placed at opposite ends of a massless beam so that the system is in equilibrium as shown. Note: The drawing is not drawn to scale. What is the value of the ratio of the lengths, b/a?

A compact disc rotates about its center at constant angular speed. Which one of the following quantities is constant and non-zero for a dust particle near the edge of the disc?

Which one of the following statements most accurately describes the center of gravity of an object?

A solid sphere rolls without slipping along a horizontal surface. What percentage of its total kinetic energy is rotational kinetic energy?

Complete the following statement: When a net torque is applied to a rigid object, it always produces a

A ceiling fan has five blades, each with a mass of 0.34 kg and a length of 0.66 m. The fan is operating in its "low" setting at which the angular speed is 9.4 rad/s. If the blades can be approximated as uniform thin rods that rotate about one end, what is the total rotational kinetic energy of the five blades?

A 4.0-kg ball moves in a straight line at 8.0 m/s as shown in the figure. At the instant shown, what is its angular momentum about the point P?

A rider on a motorcycle that has a mass of 195 kg is traveling with a speed of 24 m/s. Each of the two wheels of the motorcycle has a radius of 0.29 m and a moment of inertia of 0.46 kg . m². What is the approximate total rotational kinetic energy of the wheels?

Three objects are attached to a massless rigid rod that has an axis of rotation as shown. Assuming all of the mass of each object is located at the point shown for each, calculate the moment of inertia of this system.

A ball of mass M moves in a circular path on a horizontal, frictionless surface. It is attached to a light string that passes through a hole in the center of the table. If the string is pulled down, thereby reducing the radius of the path of the ball, the speed of the ball is observed to increase. Complete the following sentence: This occurs because

Consider the following three objects, each of the same mass and radius: All three are released from rest at the top of an inclined plane. The three objects proceed down the incline undergoing rolling motion without slipping. In which order do the objects reach the bottom of the incline?

Two equal spheres, labeled A and B in the figure, are attached to a massless rod with a frictionless pivot at the point P. The system is made to rotate clockwise with angular speed $\omega$ on a horizontal, frictionless tabletop. Sphere A collides with and sticks to another equal sphere that is at rest on the tabletop. Note: the masses of all three spheres are equal. What is the angular speed of the system immediately after the collision?

A string is wrapped around a pulley of radius 0.05 m and moment of inertia 0.2 kg . m². If the string is pulled with a force , the resulting angular acceleration of the pulley is 2 rad/s². Determine the magnitude of the force .

A massless frame in the shape of a square with 2-m sides has a 1-kg ball at each corner. What is the moment of inertia of the four balls about an axis through the corner marked O and perpendicular to the plane of the paper?

A solid sphere and a hollow sphere each of mass M and radius R are released at the same time from the top of an inclined plane. Which one of the following statements is necessarily true?

Consider the following four objects: a hoop, a flat disk, a solid sphere, and a hollow sphere. Each of the objects has mass M and radius R. The axis of rotation passes through the center of each object, and is perpendicular to the plane of the hoop and the plane of the flat disk. Which of these objects requires the largest torque to give it the same angular acceleration?

Which one of the following statements concerning the moment of inertia I is false?

A string is tied to a doorknob 0.72 m from the hinge as illustrated in the figure. At the instant shown, the force applied to the string is 5.0 N. What is the magnitude of the torque on the door?