Question 1

A car can accelerate from zero to 25 m/s in 9.5 seconds. If the diameter of the car's tire is 28 cm, the angular acceleration of the tire is

Accepted Answer

A)  89 rad/s2. 
B)  19 rad/s2. 
C)  49 rad/s2. 
D)  9.4 rad/s2. 
A)  89 rad/s2. 
B)  19 rad/s2. 
C)  49 rad/s2. 
D)  9.4 rad/s2. B

Question 2

A hollow sphere, a solid sphere, a hollow right cylinder (or hoop), and a solid right cylinder, each with the same total mass and identical maximum radius, are each rotated about their axis of symmetry. The object with the largest moment of inertia 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. C

Question 3

The mathematical relationship between the angular acceleration and the angular velocity of a body is analogous to the mathematical relationship between

Accepted Answer

A)  the angular velocity and the angle. 
B)  the angle and the angular velocity. 
C)  the angular velocity and the time. 
D)  the angle and the time. 
A)  the angular velocity and the angle. 
B)  the angle and the angular velocity. 
C)  the angular velocity and the time. 
D)  the angle and the time. A

Question 4

In many situations in physics, the order of two events does not affect the final outcome. An exception to this rule occurs for the case of

Accepted Answer

A)  two successive rotations performed on a body about different axes. 
B)  two successive translations given to a body about different axes. 
C)  two successive rotations performed on a body about the same axis. 
D)  two successive translations given to a body about the same axis. 
A)  two successive rotations performed on a body about different axes. 
B)  two successive translations given to a body about different axes. 
C)  two successive rotations performed on a body about the same axis. 
D)  two successive translations given to a body about the same axis.

Question 5

Two masses, M1 = 2.0 kg and M2 = 4.0 kg, are joined by a rigid rod of negligible mass and length 6.0 m. The moment of inertia of the system about an axis perpendicular to the rod and passing through the center of mass is

Accepted Answer

A)  12 kg·m2. 
B)  24 kg·m2. 
C)  36 kg·m2. 
D)  48 kg·m2. 
A)  12 kg·m2. 
B)  24 kg·m2. 
C)  36 kg·m2. 
D)  48 kg·m2.

Question 6

The direction of the angular momentum for an extended body lies along the axis of rotation

Accepted Answer

A)  if that axis is an axis of symmetry. 
B)  for small rotational speeds. 
C)  both of the above answers are correct. 
D)  neither of the above answers is correct. 
A)  if that axis is an axis of symmetry. 
B)  for small rotational speeds. 
C)  both of the above answers are correct. 
D)  neither of the above answers is correct.

Question 7

A wheel undergoes rotational motion according to the equation $\phi ( \mathrm { rad } ) = c t + d t ^ { 3 }$ , where $\surd$ is in radians, c = 1.0 rad/s, and d = -0.50 rad/s3. The wheel's instantaneous angular acceleration at t = 2.0 s is

Accepted Answer

A)  -6.0 rad/s2. 
B)  -3 rad/s2. 
C)  0 rad/s2. 
D)  3 rad/s2. 
A)  -6.0 rad/s2. 
B)  -3 rad/s2. 
C)  0 rad/s2. 
D)  3 rad/s2.

Question 8

A uniform solid sphere has a mass M and radius R. Its moment of inertia about an axis tangent to the surface of the sphere is:

Accepted Answer

A)  (2/5)MR2. 
B)  MR2. 
C)  (7/5)MR2. 
D)  (5/2)MR2. 
A)  (2/5)MR2. 
B)  MR2. 
C)  (7/5)MR2. 
D)  (5/2)MR2.

Question 9

An object rotates with a constant angular acceleration of 10 rad/s2, an initial angular speed of 10 rad/s, and a final angular speed of 30 rad/s. Its total time of rotation is

Accepted Answer

A)  1.0 s. 
B)  2.0 s. 
C)  3.0 s. 
D)  4.0 s. 
A)  1.0 s. 
B)  2.0 s. 
C)  3.0 s. 
D)  4.0 s.

Question 10

Dimensionally, correct relations among angle $\theta$, angular velocity $\omega$, and angular acceleration $\alpha$ include all of the following except

Accepted Answer

A)  $[ \alpha ] = [ \omega ] \cdot [ \theta ]$ 
B)  $[ \omega ] = [ \alpha ] \cdot [ \mathrm { t } ]$ 
C)  $[ \theta ] = [ \alpha ] \cdot \left[ \mathrm { t } ^ { 2 } \right]$ 
D)  $[ \omega ] = [ \alpha ] \cdot [ \theta ]$ 
A)  $[ \alpha ] = [ \omega ] \cdot [ \theta ]$ 
B)  $[ \omega ] = [ \alpha ] \cdot [ \mathrm { t } ]$ 
C)  $[ \theta ] = [ \alpha ] \cdot \left[ \mathrm { t } ^ { 2 } \right]$ 
D)  $[ \omega ] = [ \alpha ] \cdot [ \theta ]$

Question 11

An object is placed on a turntable (rotating platter) 25.0 cm from the center of rotation. The coefficient of friction between the turntable and object is 0.40. The turntable starts from rest (at time t = 0) with and is accelerated at 0.10 rad/s2. The object will begin to slide off the turntable after

Accepted Answer

A)  20 s. 
B)  40 s. 
C)  60 s. 
D)  Not enough information is given to solve this problem. 
A)  20 s. 
B)  40 s. 
C)  60 s. 
D)  Not enough information is given to solve this problem.

Question 12

A thin rod 1.0 m in length has a mass of 1.0 kg. Moving the axis of rotation will change the moment of inertia of the rod. The position, relative to the end of the rod, of the axis of rotation perpendicular to the rod for the moment of inertia to be three times the moment of inertia about an axis perpendicular to the rod passing through its center of mass is

Accepted Answer

A)  5.3 cm. 
B)  9.2 cm. 
C)  11 cm. 
D)  25 cm. 
A)  5.3 cm. 
B)  9.2 cm. 
C)  11 cm. 
D)  25 cm.

Question 13

Two point masses of 5.0 kg and 15.0 kg, separated by 2.0 m, are spinning about their combined center of mass. When the system rotates at 0.80 rad/s, the kinetic energy for the motion is

Accepted Answer

A)  5.0 J. 
B)  3.8 J. 
C)  0 J. 
D)  13 J. 
A)  5.0 J. 
B)  3.8 J. 
C)  0 J. 
D)  13 J.

Question 14

The Earth on its path around the Sun has an orbital angular momentum J and a spin angular momentum S due to its rotation about its own axis. Knowing the relationship between the year and the day, the Earth's radius, and the Earth-Sun distance, the ballpark relation between the magnitudes of J and S is

Accepted Answer

A)  J larger than S. 
B)  J approximately equal to S. 
C)  J less than S. 
D)  Hold it! Comparing these two quantities is not legitimate because they are quantities that do not have anything in common. 
A)  J larger than S. 
B)  J approximately equal to S. 
C)  J less than S. 
D)  Hold it! Comparing these two quantities is not legitimate because they are quantities that do not have anything in common.

Question 15

An object undergoes a rotation of 115° in a circular path 1.0 m in radius. The length of circular arc the object traverses is

Accepted Answer

A)  1.0 $\times$ 102 m. 
B)  2.0 m. 
C)  1.0 m. 
D)  0.0 m. 
A)  1.0 $\times$ 102 m. 
B)  2.0 m. 
C)  1.0 m. 
D)  0.0 m.

Question 16

The centripetal acceleration for a point on a rotating object is

Accepted Answer

A)  R $ \omega$ 
B)  R2  $ \omega$ 
C)  $ \omega$ /R2. 
D)  R $ \omega$ 2 . 
A)  R $ \omega$ 
B)  R2  $ \omega$ 
C)  $ \omega$ /R2. 
D)  R $ \omega$ 2 .

Question 17

A wheel undergoes rotational motion according to the equation $\phi ( \mathrm { rad } ) = c t + d t ^ { 3 }$ , where $\surd$ is in radians, c = 1.0 rad/s, and d = -0.50 rad/s3. At t = 2.0 s the centripetal acceleration of an object 10.0 cm from the center of the wheel is

Accepted Answer

A)  5.0 m/s2. 
B)  2.5 m/s2. 
C)  1.3 m/s2. 
D)  0 m/s2. 
A)  5.0 m/s2. 
B)  2.5 m/s2. 
C)  1.3 m/s2. 
D)  0 m/s2.

Question 18

An object rotates with a constant angular acceleration of 10 rad/s2, an initial angular speed of 10 rad/s, and a final angular speed of 30 rad/s. Its average angular speed is

Accepted Answer

A)  10 rad/s. 
B)  20 rad/s. 
C)  30 rad/s. 
D)  40 rad/s. 
A)  10 rad/s. 
B)  20 rad/s. 
C)  30 rad/s. 
D)  40 rad/s.

Question 19

A wheel undergoes rotational motion according to the equation $\phi ( \mathrm { rad } ) = c t + d t ^ { 3 }$ , where$\surd$ is in radians, c = 1.0 rad/s, and d = -0.50 rad/s3. The angle the wheel has turned in 2.0 s is

Accepted Answer

A)  -2.0 rad. 
B)  0 rad. 
C)  2.0 rad. 
D)  5.0 rad. 
A)  -2.0 rad. 
B)  0 rad. 
C)  2.0 rad. 
D)  5.0 rad.

Question 20

An object, starting from rest, rotates with an angular acceleration given by $\alpha = c + d t ^ { 2 }$ , where $\surd$ is in radians/s2, t is in seconds, c = -3.0 rad/s2 and d = 0.40 rad/s4. At t = 2.0 s the angular velocity of the object is

Accepted Answer

A)  -1.1 rad/s. 
B)  1.1 rad/s. 
C)  -4.9 rad/s. 
D)  -7.1 rad/s. 
A)  -1.1 rad/s. 
B)  1.1 rad/s. 
C)  -4.9 rad/s. 
D)  -7.1 rad/s.

Exam 12: Rotation of a Rigid Body

A car can accelerate from zero to 25 m/s in 9.5 seconds. If the diameter of the car's tire is 28 cm, the angular acceleration of the tire is

A hollow sphere, a solid sphere, a hollow right cylinder (or hoop), and a solid right cylinder, each with the same total mass and identical maximum radius, are each rotated about their axis of symmetry. The object with the largest moment of inertia is the

The mathematical relationship between the angular acceleration and the angular velocity of a body is analogous to the mathematical relationship between

In many situations in physics, the order of two events does not affect the final outcome. An exception to this rule occurs for the case of

Two masses, M1 = 2.0 kg and M2 = 4.0 kg, are joined by a rigid rod of negligible mass and length 6.0 m. The moment of inertia of the system about an axis perpendicular to the rod and passing through the center of mass is

The direction of the angular momentum for an extended body lies along the axis of rotation

A wheel undergoes rotational motion according to the equation ϕ(rad)=ct+dt3\phi ( \mathrm { rad } ) = c t + d t ^ { 3 }ϕ(rad)=ct+dt3 , where √\surd√ is in radians, c = 1.0 rad/s, and d = -0.50 rad/s3. The wheel's instantaneous angular acceleration at t = 2.0 s is

A uniform solid sphere has a mass M and radius R. Its moment of inertia about an axis tangent to the surface of the sphere is:

An object rotates with a constant angular acceleration of 10 rad/s2, an initial angular speed of 10 rad/s, and a final angular speed of 30 rad/s. Its total time of rotation is

Dimensionally, correct relations among angle θ\thetaθ , angular velocity ω\omegaω , and angular acceleration α\alphaα include all of the following except

Two point masses of 5.0 kg and 15.0 kg, separated by 2.0 m, are spinning about their combined center of mass. When the system rotates at 0.80 rad/s, the kinetic energy for the motion is

An object undergoes a rotation of 115° in a circular path 1.0 m in radius. The length of circular arc the object traverses is

The centripetal acceleration for a point on a rotating object is

An object rotates with a constant angular acceleration of 10 rad/s2, an initial angular speed of 10 rad/s, and a final angular speed of 30 rad/s. Its average angular speed is

A wheel undergoes rotational motion according to the equation ϕ(rad)=ct+dt3\phi ( \mathrm { rad } ) = c t + d t ^ { 3 }ϕ(rad)=ct+dt3 , where √\surd√ is in radians, c = 1.0 rad/s, and d = -0.50 rad/s3. The angle the wheel has turned in 2.0 s is

An object, starting from rest, rotates with an angular acceleration given by α=c+dt2\alpha = c + d t ^ { 2 }α=c+dt2 , where √\surd√ is in radians/s2, t is in seconds, c = -3.0 rad/s2 and d = 0.40 rad/s4. At t = 2.0 s the angular velocity of the object is

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Two masses, M₁= 2.0 kg and M₂= 4.0 kg, are joined by a rigid rod of negligible mass and length 6.0 m. The moment of inertia of the system about an axis perpendicular to the rod and passing through the center of mass is

A wheel undergoes rotational motion according to the equation $\phi ( \mathrm { rad } ) = c t + d t ^ { 3 }$ , where $\surd$ is in radians, c = 1.0 rad/s, and d = -0.50 rad/s³. The wheel's instantaneous angular acceleration at t = 2.0 s is

An object rotates with a constant angular acceleration of 10 rad/s², an initial angular speed of 10 rad/s, and a final angular speed of 30 rad/s. Its total time of rotation is

Dimensionally, correct relations among angle $\theta$ , angular velocity $\omega$ , and angular acceleration $\alpha$ include all of the following except

An object rotates with a constant angular acceleration of 10 rad/s², an initial angular speed of 10 rad/s, and a final angular speed of 30 rad/s. Its average angular speed is

A wheel undergoes rotational motion according to the equation $\phi ( \mathrm { rad } ) = c t + d t ^ { 3 }$ , where $\surd$ is in radians, c = 1.0 rad/s, and d = -0.50 rad/s³. The angle the wheel has turned in 2.0 s is

An object, starting from rest, rotates with an angular acceleration given by $\alpha = c + d t ^ { 2 }$ , where $\surd$ is in radians/s², t is in seconds, c = -3.0 rad/s² and d = 0.40 rad/s⁴. At t = 2.0 s the angular velocity of the object is