Question 1

A particle moves along the x axis. In order to calculate the torque on the particle, you need to know:

Accepted Answer

A)  the velocity of the particle 
B)  the rotational inertia of the particle 
C)  the point about which the torque is to be calculated 
D)  the kinetic energy of the particle 
E)  the mass of the particle 
A)  the velocity of the particle 
B)  the rotational inertia of the particle 
C)  the point about which the torque is to be calculated 
D)  the kinetic energy of the particle 
E)  the mass of the particle

Question 2

When the speed of a rear-drive car is increasing on a horizontal road the direction of the frictional force on the tires is:

Accepted Answer

A)  forward for all tires 
B)  backward for all tires 
C)  forward for the front tires and backward for the rear tires 
D)  backward for the front tires and forward for the rear tires 
E)  zero 
A)  forward for all tires 
B)  backward for all tires 
C)  forward for the front tires and backward for the rear tires 
D)  backward for the front tires and forward for the rear tires 
E)  zero

Question 3

A solid sphere and a solid cylinder of equal mass and radius are simultaneously released from rest on the same inclined plane sliding down the incline. Then:

Accepted Answer

A)  the sphere reaches the bottom first because it has the greater inertia 
B)  the cylinder reaches the bottom first because it picks up more rotational energy 
C)  the sphere reaches the bottom first because it picks up more rotational energy 
D)  they reach the bottom together 
E)  none of the above is true 
A)  the sphere reaches the bottom first because it has the greater inertia 
B)  the cylinder reaches the bottom first because it picks up more rotational energy 
C)  the sphere reaches the bottom first because it picks up more rotational energy 
D)  they reach the bottom together 
E)  none of the above is true

Question 4

A yo-yo, arranged as shown, rests on a frictionless surface. When a force is applied to the string as shown, the yo-yo:

Accepted Answer

A)  moves to the left and rotates counterclockwise 
B)  moves to the right and rotates counterclockwise 
C)  moves to the left and rotates clockwise 
D)  moves to the right and rotates clockwise 
E)  moves to the right and does not rotate 
A)  moves to the left and rotates counterclockwise 
B)  moves to the right and rotates counterclockwise 
C)  moves to the left and rotates clockwise 
D)  moves to the right and rotates clockwise 
E)  moves to the right and does not rotate

Question 5

A solid wheel with mass M, radius R, and rotational inertia MR2/2, rolls without sliding on a horizontal surface. A horizontal force F is applied to the axle and the center of mass has an acceleration a. The magnitudes of the applied force F and the frictional force f of the surface, respectively, are:

Accepted Answer

A)  F = Ma, f = 0 
B)  F = Ma, f = Ma/2 
C)  F = 2Ma, f = Ma 
D)  F = 2Ma, f = Ma/2 
E)  F = 3Ma/2, f = Ma/2 
A)  F = Ma, f = 0 
B)  F = Ma, f = Ma/2 
C)  F = 2Ma, f = Ma 
D)  F = 2Ma, f = Ma/2 
E)  F = 3Ma/2, f = Ma/2

Question 6

The newton.second is a unit of:

Accepted Answer

A)  work 
B)  angular momentum 
C)  power 
D)  linear momentum 
E)  none of these 
A)  work 
B)  angular momentum 
C)  power 
D)  linear momentum 
E)  none of these

Question 7

A single force acts on a particle P. Rank each of the orientations of the force shown below according to the magnitude of the time rate of change of the particle's angular momentum about the point O, least to greatest.

Accepted Answer

A)  1, 2, 3, 4 
B)  1 and 2 tie, then 3, then 4 
C)  1 and 2 tie, then 4, then 3 
D)  1 and 2 tie, then 3 and 4 tie 
E)  All are the same 
A)  1, 2, 3, 4 
B)  1 and 2 tie, then 3, then 4 
C)  1 and 2 tie, then 4, then 3 
D)  1 and 2 tie, then 3 and 4 tie 
E)  All are the same

Question 8

The angular momentum vector of Earth, due to its daily rotation, is directed:

Accepted Answer

A)  tangent to the equator toward the east 
B)  tangent to the equator toward the west 
C)  north 
D)  south 
E)  toward the sun 
A)  tangent to the equator toward the east 
B)  tangent to the equator toward the west 
C)  north 
D)  south 
E)  toward the sun

Question 9

A man, holding a weight in each hand, stands at the center of a horizontal frictionless rotating turntable. The effect of the weights is to double the rotational inertia of the system. As he is rotating, the man opens his hands and drops the two weights. They fall outside the turntable. Then:

Accepted Answer

A)  his angular velocity doubles 
B)  his angular velocity remains about the same 
C)  his angular velocity is halved 
D)  the direction of his angular momentum vector changes 
E)  his rotational kinetic energy increases 
A)  his angular velocity doubles 
B)  his angular velocity remains about the same 
C)  his angular velocity is halved 
D)  the direction of his angular momentum vector changes 
E)  his rotational kinetic energy increases

Question 10

A wheel of radius 0.5 m rolls without sliding on a horizontal surface as shown. Starting from rest, the wheel moves with constant angular acceleration 6 rad/s2. The distance in traveled by the center of the wheel from t = 0 to t = 3 s is:

Accepted Answer

A)  0 m 
B)  27 m 
C)  13.5 m 
D)  18 m 
E)  none of these 
A)  0 m 
B)  27 m 
C)  13.5 m 
D)  18 m 
E)  none of these

Question 11

As a 2.0-kg block travels around a 0.50-m radius circle it has an angular speed of 12 rad/s. The circle is parallel to the xy plane and is centered on the z axis, 0.75 m from the origin. The magnitude of its angular momentum around the origin is:

Accepted Answer

A)  6.0 kg∙m2/s 
B)  9.0 kg∙m2/s 
C)  11 kg∙m2/s 
D)  14 kg∙m2/s 
E)  20 kg∙m2/s 
A)  6.0 kg∙m2/s 
B)  9.0 kg∙m2/s 
C)  11 kg∙m2/s 
D)  14 kg∙m2/s 
E)  20 kg∙m2/s

Question 12

A particle is located on the x axis at x = 2.0 m from the origin. A force of 25 N, directed 30° above the x axis in the x-y plane, acts on the particle. What is the torque about the origin on the particle?

Accepted Answer

A)  50 N∙m, in the positive z direction 
B)  25 N∙m, in the positive z direction 
C)  50 N∙m, in the negative z direction 
D)  25 N∙m, in the negative z direction 
E)  There is no torque about the origin. 
A)  50 N∙m, in the positive z direction 
B)  25 N∙m, in the positive z direction 
C)  50 N∙m, in the negative z direction 
D)  25 N∙m, in the negative z direction 
E)  There is no torque about the origin.

Question 13

A solid sphere starts from rest and rolls down a slope that is 5.1 m long. If its speed at the bottom of the slope is 4.3 m/s, what is the angle of the slope?

Accepted Answer

A)  10° 
B)  15° 
C)  20° 
D)  30° 
E)  cannot be calculated without knowing the mass and radius of the sphere 
A)  10° 
B)  15° 
C)  20° 
D)  30° 
E)  cannot be calculated without knowing the mass and radius of the sphere

Question 14

Two uniform cylinders have different masses and different rotational inertias. They simultaneously start from rest at the top of an inclined plane and roll without sliding down the plane. The cylinder that gets to the bottom first is:

Accepted Answer

A)  the one with the larger mass 
B)  the one with the smaller mass 
C)  the one with the larger rotational inertia 
D)  the one with the smaller rotational inertia 
E)  neither (they arrive together) 
A)  the one with the larger mass 
B)  the one with the smaller mass 
C)  the one with the larger rotational inertia 
D)  the one with the smaller rotational inertia 
E)  neither (they arrive together)

Question 15

A rod rests on frictionless ice. Forces that are equal in magnitude and opposite in direction are simultaneously applied to its ends as shown. The quantity that has a magnitude of zero is its:

Accepted Answer

A)  angular momentum 
B)  angular acceleration 
C)  total linear momentum 
D)  kinetic energy 
E)  rotational inertia 
A)  angular momentum 
B)  angular acceleration 
C)  total linear momentum 
D)  kinetic energy 
E)  rotational inertia

Question 16

A playground merry-go-round has a radius of 3.0 m and a rotational inertia of 600 kg∙m2. It is initially spinning at 0.80 rad/s when a 20-kg child crawls from the center to the rim. When the child reaches the rim the angular velocity of the merry-go-round is:

Accepted Answer

A)  0.62 rad/s 
B)  0.73 rad/s 
C)  0.77 rad/s 
D)  0.91 rad/s 
E)  1.1 rad/s 
A)  0.62 rad/s 
B)  0.73 rad/s 
C)  0.77 rad/s 
D)  0.91 rad/s 
E)  1.1 rad/s

Question 17

A simple gyroscope consists of a wheel (M = 2.0 kg, R = 0.75 m, I = 1.1 kg∙m2) rotating on a horizontal shaft. If the shaft is balanced on a pivot 0.50 m from the wheel, and the wheel rotates at 500 rev/min, what is the precession frequency of the wheel?

Accepted Answer

A)  1.8 x 10-2 rad/s 
B)  2.7 x 10-2 rad/s 
C)  0.17 rad/s 
D)  0.26 rad/s 
E)  0.50 rad/s 
A)  1.8 x 10-2 rad/s 
B)  2.7 x 10-2 rad/s 
C)  0.17 rad/s 
D)  0.26 rad/s 
E)  0.50 rad/s

Question 18

A playground merry-go-round has a radius R and a rotational inertia I. When the merry-go-round is at rest, a child with mass m runs with speed v along a line tangent to the rim and jumps on. The angular velocity of the merry-go-round is then:

Accepted Answer

A)  mv/I 
B)  v/R 
C)  mRv/I 
D)  2mRv/I 
E)  mRv/(mR2 + I) 
A)  mv/I 
B)  v/R 
C)  mRv/I 
D)  2mRv/I 
E)  mRv/(mR2 + I)

Question 19

A wheel rolls without slipping along a horizontal road as shown. The velocity of the center of the wheel is represented by . Point P is painted on the rim of the wheel. The direction of the instantaneous velocity of point P is:

Accepted Answer

A)  $\rightarrow$ 
B)  $\leftarrow$ 
C)  $\uparrow$ 
D)    
E)  zero 
A)  $\rightarrow$ 
B)  $\leftarrow$ 
C)  $\uparrow$ 
D)    
E)  zero

Question 20

A simple gyroscope consists of a wheel (R = 0.75 m, I = 0.9 MR2) rotating on a horizontal shaft. If the shaft is balanced on a pivot 0.50 m from the wheel, and the wheel rotates at 500 rev/min, what is the precession frequency of the wheel?

Accepted Answer

A)  1.9 x 10-2 rad/s 
B)  2.9 x 10-2 rad/s 
C)  0.19 rad/s 
D)  0.28 rad/s 
E)  cannot be calculated without knowing the mass of the wheel 
A)  1.9 x 10-2 rad/s 
B)  2.9 x 10-2 rad/s 
C)  0.19 rad/s 
D)  0.28 rad/s 
E)  cannot be calculated without knowing the mass of the wheel

Exam 11: Rolling, Torque, and Angular Momentum

A particle moves along the x axis. In order to calculate the torque on the particle, you need to know:

When the speed of a rear-drive car is increasing on a horizontal road the direction of the frictional force on the tires is:

A solid sphere and a solid cylinder of equal mass and radius are simultaneously released from rest on the same inclined plane sliding down the incline. Then:

A yo-yo, arranged as shown, rests on a frictionless surface. When a force is applied to the string as shown, the yo-yo:

The newton.second is a unit of:

A single force acts on a particle P. Rank each of the orientations of the force shown below according to the magnitude of the time rate of change of the particle's angular momentum about the point O, least to greatest.

The angular momentum vector of Earth, due to its daily rotation, is directed:

A man, holding a weight in each hand, stands at the center of a horizontal frictionless rotating turntable. The effect of the weights is to double the rotational inertia of the system. As he is rotating, the man opens his hands and drops the two weights. They fall outside the turntable. Then:

A wheel of radius 0.5 m rolls without sliding on a horizontal surface as shown. Starting from rest, the wheel moves with constant angular acceleration 6 rad/s2. The distance in traveled by the center of the wheel from t = 0 to t = 3 s is:

As a 2.0-kg block travels around a 0.50-m radius circle it has an angular speed of 12 rad/s. The circle is parallel to the xy plane and is centered on the z axis, 0.75 m from the origin. The magnitude of its angular momentum around the origin is:

A particle is located on the x axis at x = 2.0 m from the origin. A force of 25 N, directed 30° above the x axis in the x-y plane, acts on the particle. What is the torque about the origin on the particle?

A solid sphere starts from rest and rolls down a slope that is 5.1 m long. If its speed at the bottom of the slope is 4.3 m/s, what is the angle of the slope?

Two uniform cylinders have different masses and different rotational inertias. They simultaneously start from rest at the top of an inclined plane and roll without sliding down the plane. The cylinder that gets to the bottom first is:

A rod rests on frictionless ice. Forces that are equal in magnitude and opposite in direction are simultaneously applied to its ends as shown. The quantity that has a magnitude of zero is its:

A playground merry-go-round has a radius of 3.0 m and a rotational inertia of 600 kg∙m2. It is initially spinning at 0.80 rad/s when a 20-kg child crawls from the center to the rim. When the child reaches the rim the angular velocity of the merry-go-round is:

A simple gyroscope consists of a wheel (M = 2.0 kg, R = 0.75 m, I = 1.1 kg∙m2) rotating on a horizontal shaft. If the shaft is balanced on a pivot 0.50 m from the wheel, and the wheel rotates at 500 rev/min, what is the precession frequency of the wheel?

A playground merry-go-round has a radius R and a rotational inertia I. When the merry-go-round is at rest, a child with mass m runs with speed v along a line tangent to the rim and jumps on. The angular velocity of the merry-go-round is then:

A wheel rolls without slipping along a horizontal road as shown. The velocity of the center of the wheel is represented by . Point P is painted on the rim of the wheel. The direction of the instantaneous velocity of point P is:

A simple gyroscope consists of a wheel (R = 0.75 m, I = 0.9 MR2) rotating on a horizontal shaft. If the shaft is balanced on a pivot 0.50 m from the wheel, and the wheel rotates at 500 rev/min, what is the precession frequency of the wheel?

Measurement

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Vector

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Kinetic Energy and Work

Potential Energy and Conservation of Energy

Center of Mass and Linear Momentum

Rotation

Equilibrium and Elasticity

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The Kinetic Theory of Gases

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Maxwells Equations; Magnetism of Matter

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More About Matter Waves

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Energy From the Nucleus

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Filters

A wheel of radius 0.5 m rolls without sliding on a horizontal surface as shown. Starting from rest, the wheel moves with constant angular acceleration 6 rad/s². The distance in traveled by the center of the wheel from t = 0 to t = 3 s is:

A playground merry-go-round has a radius of 3.0 m and a rotational inertia of 600 kg∙m². It is initially spinning at 0.80 rad/s when a 20-kg child crawls from the center to the rim. When the child reaches the rim the angular velocity of the merry-go-round is:

A simple gyroscope consists of a wheel (M = 2.0 kg, R = 0.75 m, I = 1.1 kg∙m²) rotating on a horizontal shaft. If the shaft is balanced on a pivot 0.50 m from the wheel, and the wheel rotates at 500 rev/min, what is the precession frequency of the wheel?

A simple gyroscope consists of a wheel (R = 0.75 m, I = 0.9 MR²) rotating on a horizontal shaft. If the shaft is balanced on a pivot 0.50 m from the wheel, and the wheel rotates at 500 rev/min, what is the precession frequency of the wheel?