Question 1

A wheel rotating at 7.5 rad/s slows down at 0.50 rad/s2. The number of revolutions made by the wheel in the first 10 s is

Accepted Answer

A)  50 revolutions. 
B)  38 revolutions. 
C)  20 revolutions. 
D)  7.9 revolutions. 
E)  0.38 revolutions. 
A)  50 revolutions. 
B)  38 revolutions. 
C)  20 revolutions. 
D)  7.9 revolutions. 
E)  0.38 revolutions.

Question 2

A wheel of moment of inertia of 300 kg.m2 initially at rest is accelerated by a constant torque of 5.00 N.m over 9.00 s. The wheel's rotational kinetic energy at the end of the 9.00 s is

Accepted Answer

A)  0.150 J. 
B)  0.296 J. 
C)  1.00 J. 
D)  3.38 J. 
E)  6.67 J. 
A)  0.150 J. 
B)  0.296 J. 
C)  1.00 J. 
D)  3.38 J. 
E)  6.67 J.

Question 3

A solid cylinder of mass 10 kg and radius 1.0 m rotates about its own symmetry axis. A rope wrapped around it exerts a 5.0-N force tangent to the cylinder, causing the cylinder to rotate clockwise. A second rope wrapped around another section of the same cylinder exerts a 6.0-N force that is tangent to the cylinder, causing the cylinder to rotate counterclockwise. The magnitude of the cylinder's angular acceleration is

Accepted Answer

A)  0.20 rad/s2. 
B)  0.91 rad/s2. 
C)  1.1 rad/s2. 
D)  10 rad/s2. 
E)  11 rad/s2. 
A)  0.20 rad/s2. 
B)  0.91 rad/s2. 
C)  1.1 rad/s2. 
D)  10 rad/s2. 
E)  11 rad/s2.

Question 4

Consider an Atwood machine with m2 > m1 and a pulley of mass M. The acceleration of the system, compared to the case when the pulley's mass is negligible, is

Accepted Answer

A)  larger than the acceleration of the same system when the pulley's mass is negligible. 
B)  smaller than the acceleration of the same system when the pulley's mass is negligible. 
C)  equal to the acceleration of the same system when the pulley's mass is negligible. 
D)  unknown; more information is needed to work out the answer. 
A)  larger than the acceleration of the same system when the pulley's mass is negligible. 
B)  smaller than the acceleration of the same system when the pulley's mass is negligible. 
C)  equal to the acceleration of the same system when the pulley's mass is negligible. 
D)  unknown; more information is needed to work out the answer.

Question 5

A disk of moment of inertia 80 kg.m2 is free to rotate about its axis (through the center, perpendicular to the plane of the disk, which is set vertical). To increase its angular velocity uniformly from rest to 5.0 rad/s in 20.0 s, the torque applied is

Accepted Answer

A)  8.0 * 103 N.m. 
B)  3.2 *102 N.m. 
C)  20 N.m. 
D)  32 N.m. 
E)  0.80 N.m. 
A)  8.0 * 103 N.m. 
B)  3.2 *102 N.m. 
C)  20 N.m. 
D)  32 N.m. 
E)  0.80 N.m.

Question 6

A solid cylinder (the moment of inertia about its axis is mr2/2) rolls without slipping. The ratio of its rotational to translational kinetic energy is

Accepted Answer

A)  1/4. 
B)  1/2. 
C)  1. 
D)  2. 
E)  4. 
A)  1/4. 
B)  1/2. 
C)  1. 
D)  2. 
E)  4.

Question 7

You are sitting on a stool that can rotate friction-free about its vertical axis, holding a spinning bicycle wheel that rotates in a horizontal plane. When you flip the bicycle wheel (turn it over through 180o), you will

Accepted Answer

A)  rotate in the same direction the bicycle wheel was originally rotating. 
B)  stay still. 
C)  rotate in the direction opposite to that of the bicycle wheel's original rotation. 
A)  rotate in the same direction the bicycle wheel was originally rotating. 
B)  stay still. 
C)  rotate in the direction opposite to that of the bicycle wheel's original rotation.

Question 8

A top is spinning rapidly on a table, its axis inclined to the vertical. If only the angle of inclination is changed, each of the following quantities changes except the

Accepted Answer

A)  torque. 
B)  precession frequency. 
C)  angular momentum. 
D)  precessional angular velocity. 
A)  torque. 
B)  precession frequency. 
C)  angular momentum. 
D)  precessional angular velocity.

Question 9

A hollow sphere and a solid sphere each made from the same material and having equal maximum radius are rolled from rest (without slipping) the same distance down an inclined plane. The torque experienced by the hollow sphere is

Accepted Answer

A)  smaller than the torque experienced by the solid sphere. 
B)  larger than the torque experienced by the solid sphere. 
C)  the same as the torque experienced by the solid sphere. 
D)  unknown; more information is needed to work out the answer. 
A)  smaller than the torque experienced by the solid sphere. 
B)  larger than the torque experienced by the solid sphere. 
C)  the same as the torque experienced by the solid sphere. 
D)  unknown; more information is needed to work out the answer.

Question 10

A diver can reduce her moment of inertia by a factor of about 3.14 when changing from the straight position to the tuck position. If she makes 3.0 rotations in 2.0 s when in the tuck position, her angular speed when in the straight position is

Accepted Answer

A)  0.48 rad/s. 
B)  0.52 rad/s. 
C)  3.0 rad/s. 
D)  4.7 rad/s. 
E)  30 rad/s. 
A)  0.48 rad/s. 
B)  0.52 rad/s. 
C)  3.0 rad/s. 
D)  4.7 rad/s. 
E)  30 rad/s.

Question 11

A pencil of mass M and length L has a moment of inertia about its center of mass of (1/12) M L2 (assume uniform mass distribution). It balances vertically on the eraser in a state of unstable equilibrium. A fly of mass m is perched on the other end. Assuming the fly hangs on and the eraser does not slip, the kinetic energy of the system just before it hits the desk is

Accepted Answer

A)  (M + m)gL. 
B)  1/2(2M + m)gL. 
C)  1/2(M + m)gL. 
D)  1/2(M + 2m)gL. 
E)  2(M + m)gL. 
A)  (M + m)gL. 
B)  1/2(2M + m)gL. 
C)  1/2(M + m)gL. 
D)  1/2(M + 2m)gL. 
E)  2(M + m)gL.

Question 12

A bowling ball of mass 6.0 kg and radius 9.0 cm rolls without slipping down a lane at 4.0 m/s. The total kinetic energy of the bowling ball is

Accepted Answer

A)  19 J. 
B)  24 J. 
C)  48 J. 
D)  67 J. 
E)  96 J. 
A)  19 J. 
B)  24 J. 
C)  48 J. 
D)  67 J. 
E)  96 J.

Question 13

A 10-N force is applied tangent to a wheel of radius R, while a 15-N force is applied tangent to a wheel of radius R/3 mounted on top of the previous wheel, as pictured here. The torque acting on the system is

Accepted Answer

A)  5R in the negative x direction. 
B)  5R in the positive x direction. 
C)  5R in the negative y direction. 
D)  5R in the positive y direction. 
E)  5R in the xz plane. 
A)  5R in the negative x direction. 
B)  5R in the positive x direction. 
C)  5R in the negative y direction. 
D)  5R in the positive y direction. 
E)  5R in the xz plane.

Question 14

The work done in rotating a rigid body can be expressed as

Accepted Answer

A)  the scalar product between the torque applied and the angular displacement. 
B)  the vector product between the torque applied and the angular displacement. 
C)  the product between the magnitude of the torque applied and the angular displacement. 
D)  the scalar product between the force applied and the lever arm. 
E)  the vector product between the force applied and the lever arm. 
A)  the scalar product between the torque applied and the angular displacement. 
B)  the vector product between the torque applied and the angular displacement. 
C)  the product between the magnitude of the torque applied and the angular displacement. 
D)  the scalar product between the force applied and the lever arm. 
E)  the vector product between the force applied and the lever arm.

Question 15

A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/min. When turned off, it rotates 20.0 times at a constant angular acceleration before coming to rest. The time necessary for the centrifuge to come to rest is

Accepted Answer

A)  0.66 s. 
B)  6.6 s. 
C)  66 s. 
D)  2.5 * 102 s. 
E)  5.7 * 102 s. 
A)  0.66 s. 
B)  6.6 s. 
C)  66 s. 
D)  2.5 * 102 s. 
E)  5.7 * 102 s.

Question 16

A hollow sphere, a solid sphere, a hollow right cylinder (or hoop), and a solid right cylinder having the same total mass and identical maximum radius are rolled (without slipping) the same distance down an inclined plane. The object with the shortest travel time is the

Accepted Answer

A)  hollow sphere. 
B)  solid sphere. 
C)  hollow right cylinder (or hoop). 
D)  solid right cylinder. 
A)  hollow sphere. 
B)  solid sphere. 
C)  hollow right cylinder (or hoop). 
D)  solid right cylinder.

Question 17

A uniform thin rod of length 0.40 m and mass 4.0 kg can rotate in the horizontal plane about a vertical axis through one end. The rod is at rest when a 3.0-g bullet traveling in the horizontal plane of the rod is fired into the free end of the rod. As viewed from above, the direction of the bullet's velocity makes an angle of 60o with the rod. The bullet lodges in the rod, and the angular velocity of the rod is 10 rad/s immediately after collision. The magnitude of the bullet's velocity just before impact was

Accepted Answer

A)  2.1 $\times$ 102 m/s. 
B)  1.8 $\times$ 103 m/s. 
C)  3.6 $\times$ 103 m/s. 
D)  1.8 $\times$ 104 m/s. 
E)  2.1 $\times$ 104 m/s. 
A)  2.1 $\times$ 102 m/s. 
B)  1.8 $\times$ 103 m/s. 
C)  3.6 $\times$ 103 m/s. 
D)  1.8 $\times$ 104 m/s. 
E)  2.1 $\times$ 104 m/s.

Question 18

You are sitting on a stool that can rotate friction-free about its vertical axis, holding a mass in each outstretched hand. When you suddenly release and drop the masses, your angular velocity

Accepted Answer

A)  increases. 
B)  stays the same. 
C)  decreases. 
D)  becomes zero. 
A)  increases. 
B)  stays the same. 
C)  decreases. 
D)  becomes zero.

Question 19

The Earth moves about the Sun in an elliptical orbit. As the Earth moves closer to the Sun, the angular speed of the Earth about the Sun

Accepted Answer

A)  increases. 
B)  stays the same. 
C)  decreases. 
D)  is zero. 
A)  increases. 
B)  stays the same. 
C)  decreases. 
D)  is zero.

Question 20

From a torque applied versus angular acceleration graph for the rotation of a rigid body about a fixed axis, the body's moment of inertia can be calculated as

Accepted Answer

A)  the value of the torque divided by the value of the angular acceleration at a certain instant. 
B)  the value of the torque multiplied by the value of the angular acceleration at a certain instant. 
C)  the area bounded by the curve and the torque axis. 
D)  the area bounded by the curve and the angular acceleration axis. 
E)  the slope of the curve. 
A)  the value of the torque divided by the value of the angular acceleration at a certain instant. 
B)  the value of the torque multiplied by the value of the angular acceleration at a certain instant. 
C)  the area bounded by the curve and the torque axis. 
D)  the area bounded by the curve and the angular acceleration axis. 
E)  the slope of the curve.

Exam 13: Dynamics of a Rigid Body

A wheel rotating at 7.5 rad/s slows down at 0.50 rad/s2. The number of revolutions made by the wheel in the first 10 s is

A wheel of moment of inertia of 300 kg.m2 initially at rest is accelerated by a constant torque of 5.00 N.m over 9.00 s. The wheel's rotational kinetic energy at the end of the 9.00 s is

Consider an Atwood machine with m2 > m1 and a pulley of mass M. The acceleration of the system, compared to the case when the pulley's mass is negligible, is

A disk of moment of inertia 80 kg.m2 is free to rotate about its axis (through the center, perpendicular to the plane of the disk, which is set vertical). To increase its angular velocity uniformly from rest to 5.0 rad/s in 20.0 s, the torque applied is

A solid cylinder (the moment of inertia about its axis is mr2/2) rolls without slipping. The ratio of its rotational to translational kinetic energy is

You are sitting on a stool that can rotate friction-free about its vertical axis, holding a spinning bicycle wheel that rotates in a horizontal plane. When you flip the bicycle wheel (turn it over through 180o), you will

A top is spinning rapidly on a table, its axis inclined to the vertical. If only the angle of inclination is changed, each of the following quantities changes except the

A hollow sphere and a solid sphere each made from the same material and having equal maximum radius are rolled from rest (without slipping) the same distance down an inclined plane. The torque experienced by the hollow sphere is

A diver can reduce her moment of inertia by a factor of about 3.14 when changing from the straight position to the tuck position. If she makes 3.0 rotations in 2.0 s when in the tuck position, her angular speed when in the straight position is

A bowling ball of mass 6.0 kg and radius 9.0 cm rolls without slipping down a lane at 4.0 m/s. The total kinetic energy of the bowling ball is

A 10-N force is applied tangent to a wheel of radius R, while a 15-N force is applied tangent to a wheel of radius R/3 mounted on top of the previous wheel, as pictured here. The torque acting on the system is

The work done in rotating a rigid body can be expressed as

A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/min. When turned off, it rotates 20.0 times at a constant angular acceleration before coming to rest. The time necessary for the centrifuge to come to rest is

A hollow sphere, a solid sphere, a hollow right cylinder (or hoop), and a solid right cylinder having the same total mass and identical maximum radius are rolled (without slipping) the same distance down an inclined plane. The object with the shortest travel time is the

You are sitting on a stool that can rotate friction-free about its vertical axis, holding a mass in each outstretched hand. When you suddenly release and drop the masses, your angular velocity

The Earth moves about the Sun in an elliptical orbit. As the Earth moves closer to the Sun, the angular speed of the Earth about the Sun

From a torque applied versus angular acceleration graph for the rotation of a rigid body about a fixed axis, the body's moment of inertia can be calculated as

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A wheel rotating at 7.5 rad/s slows down at 0.50 rad/s². The number of revolutions made by the wheel in the first 10 s is

A wheel of moment of inertia of 300 kg.m² initially at rest is accelerated by a constant torque of 5.00 N.m over 9.00 s. The wheel's rotational kinetic energy at the end of the 9.00 s is

Consider an Atwood machine with m₂> m₁and a pulley of mass M. The acceleration of the system, compared to the case when the pulley's mass is negligible, is

A disk of moment of inertia 80 kg.m² is free to rotate about its axis (through the center, perpendicular to the plane of the disk, which is set vertical). To increase its angular velocity uniformly from rest to 5.0 rad/s in 20.0 s, the torque applied is

A solid cylinder (the moment of inertia about its axis is mr²/2) rolls without slipping. The ratio of its rotational to translational kinetic energy is

You are sitting on a stool that can rotate friction-free about its vertical axis, holding a spinning bicycle wheel that rotates in a horizontal plane. When you flip the bicycle wheel (turn it over through 180^o), you will