Question 1

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

Accepted Answer

A) 33 % 
B) 50 % 
C) 12 % 
D) 75 % 
E) 29 % 
A) 33 % 
B) 50 % 
C) 12 % 
D) 75 % 
E) 29 %

Question 2

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?

Accepted Answer

A) $\omega$ 
B) 0.82$\omega$ 
C) 0.60$\omega$ 
D) 0.56$\omega$ 
E) 0.29$\omega$ 
A) $\omega$ 
B) 0.82$\omega$ 
C) 0.60$\omega$ 
D) 0.56$\omega$ 
E) 0.29$\omega$

Question 3

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

Accepted Answer

A) I may be expressed in units of kg .m2. 
B) I depends on the angular acceleration of the object as it rotates. 
C) I depends on the location of the rotation axis relative to the particles that make up the object. 
D) I depends on the orientation of the rotation axis relative to the particles that make up the object. 
E) Of the particles that make up an object, the particle with the smallest mass may contribute the greatest amount to I. 
A) I may be expressed in units of kg .m2. 
B) I depends on the angular acceleration of the object as it rotates. 
C) I depends on the location of the rotation axis relative to the particles that make up the object. 
D) I depends on the orientation of the rotation axis relative to the particles that make up the object. 
E) Of the particles that make up an object, the particle with the smallest mass may contribute the greatest amount to I.

Question 4

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?

Accepted Answer

A) 2.1 N. m 
B) 3.0 N . m 
C) 1.0 N . m 
D) 0.78 N . m 
E) 0.60 N . m 
A) 2.1 N. m 
B) 3.0 N . m 
C) 1.0 N . m 
D) 0.78 N . m 
E) 0.60 N . m

Question 5

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   .

Accepted Answer

A) 0.4 N 
B) 2 N 
C) 8 N 
D) 16 N 
E) 40 N 
A) 0.4 N 
B) 2 N 
C) 8 N 
D) 16 N 
E) 40 N

Question 6

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,

Accepted Answer

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. 
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.

Question 7

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?

Accepted Answer

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

Question 8

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?

Accepted Answer

A) 2.0 
B) 2.5 
C) 3.0 
D) 4.0 
E) 5.0 
A) 2.0 
B) 2.5 
C) 3.0 
D) 4.0 
E) 5.0

Question 9

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?

Accepted Answer

A) 3, 1, 2 
B) 2, 3, 1 
C) 1, 2, 3 
D) 3, 2, 1 
E) All three reach the bottom at the same time. 
A) 3, 1, 2 
B) 2, 3, 1 
C) 1, 2, 3 
D) 3, 2, 1 
E) All three reach the bottom at the same time.

Question 10

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.

Accepted Answer

A) 1.3 kg . m2 
B) 3.1 kg . m2 
C) 5.3 kg . m2 
D) 7.2 kg . m2 
E) 9.1 kg . m2 
A) 1.3 kg . m2 
B) 3.1 kg . m2 
C) 5.3 kg . m2 
D) 7.2 kg . m2 
E) 9.1 kg . m2

Question 11

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?

Accepted Answer

A) the solid sphere 
B) the hollow sphere 
C) the hoop 
D) the flat disk 
E) both the solid and the hollow spheres 
A) the solid sphere 
B) the hollow sphere 
C) the hoop 
D) the flat disk 
E) both the solid and the hollow spheres

Question 12

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?

Accepted Answer

A) 4 kg . m2 
B) 8 kg . m2 
C) 10 kg . m2 
D) 12 kg . m2 
E) 16 kg . m2 
A) 4 kg . m2 
B) 8 kg . m2 
C) 10 kg . m2 
D) 12 kg . m2 
E) 16 kg . m2

Question 13

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?

Accepted Answer

A) 35 J 
B) 29 J 
C) 23 J 
D) 17 J 
E) 11 J 
A) 35 J 
B) 29 J 
C) 23 J 
D) 17 J 
E) 11 J

Question 14

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?

Accepted Answer

A) linear velocity 
B) torque about the center of the disc 
C) centripetal acceleration 
D) angular momentum 
E) angular acceleration 
A) linear velocity 
B) torque about the center of the disc 
C) centripetal acceleration 
D) angular momentum 
E) angular acceleration

Question 15

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

Accepted Answer

A) the linear momentum of the ball is conserved. 
B) it is required by Newton's first law of motion. 
C) the angular momentum of the ball is conserved. 
D) the angular momentum of the ball must increase. 
E) the total mechanical energy of the ball must remain constant. 
A) the linear momentum of the ball is conserved. 
B) it is required by Newton's first law of motion. 
C) the angular momentum of the ball is conserved. 
D) the angular momentum of the ball must increase. 
E) the total mechanical energy of the ball must remain constant.

Question 16

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?

Accepted Answer

A) The solid sphere will reach the bottom first. 
B) The hollow sphere will reach the bottom first. 
C) Both spheres will reach the bottom at the same time. 
D) The solid sphere will reach the bottom with the greater kinetic energy. 
E) The hollow sphere will reach the bottom with the greater kinetic energy. 
A) The solid sphere will reach the bottom first. 
B) The hollow sphere will reach the bottom first. 
C) Both spheres will reach the bottom at the same time. 
D) The solid sphere will reach the bottom with the greater kinetic energy. 
E) The hollow sphere will reach the bottom with the greater kinetic energy.

Question 17

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?

Accepted Answer

A) 800 J 
B) 1100 J 
C) 1500 J 
D) 3200 J 
E) 4100 J 
A) 800 J 
B) 1100 J 
C) 1500 J 
D) 3200 J 
E) 4100 J

Question 18

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

Accepted Answer

A) It is the point where gravity acts on the object. 
B) It is the point where all the mass is concentrated. 
C) It must be experimentally determined for all objects. 
D) It is the point on the object where all the weight is concentrated. 
E) It is the point from which the torque produced by the weight of the object can be calculated. 
A) It is the point where gravity acts on the object. 
B) It is the point where all the mass is concentrated. 
C) It must be experimentally determined for all objects. 
D) It is the point on the object where all the weight is concentrated. 
E) It is the point from which the torque produced by the weight of the object can be calculated.

Question 19

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

Accepted Answer

A) constant acceleration. 
B) rotational equilibrium. 
C) constant angular velocity. 
D) constant angular momentum. 
E) change in angular velocity. 
A) constant acceleration. 
B) rotational equilibrium. 
C) constant angular velocity. 
D) constant angular momentum. 
E) change in angular velocity.

Question 20

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?

Accepted Answer

A) 33 kg . m2/s 
B) 85 kg . m2/s 
C) 110 kg . m2/s 
D) 160 kg . m2/s 
E) zero kg . m2/s 
A) 33 kg . m2/s 
B) 85 kg . m2/s 
C) 110 kg . m2/s 
D) 160 kg . m2/s 
E) zero kg . m2/s

Exam 9: Rotational Dynamics

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

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?

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 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 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 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?

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?

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 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 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?

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?

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?

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

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

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?

Introduction and Mathematical Concepts

Kinematics in One Dimension

Kinematics in Two Dimensions

Forces and Newtons Laws of Motion

Dynamics of Uniform Circular Motion

Work and Energy

Impulse and Momentum

Rotational Kinematics

Simple Harmonic Motion and Elasticity

Fluids

Temperature and Heat

The Transfer of Heat

The Ideal Gas Law and Kinetic Theory

Thermodynamics

Waves and Sound

The Principle of Linear Superposition and Interference Phenomena

Electric Forces and Electric Fields

Electric Potential Energy and the Electric Potential

Electric Circuits

Magnetic Forces and Magnetic Fields

Electromagnetic Induction

Alternating Current Circuits

Electromagnetic Waves

The Refl Ection of Light: Mirrors

The Refraction of Light: Lenses and Optical Instruments

Interference and the Wave Nature of Light

Special Relativity

Particles and Waves

The Nature of the Atom

Nuclear Physics and Radioactivity

Ionizing Radiation, Nuclear Energy, and Elementary Particles

Filters

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 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?