Question 1

a hoop in the x,y plane The order of increasing rotational inertia about an axis through the center of mass and parallel to the z axis is:

Accepted Answer

A)  1, 2, 3, 4 
B)  4, 3, 2, 1 
C)  1, 3, 2, 4 
D)  4, 2, 3, 1 
E)  3, 1, 2, 4 
A)  1, 2, 3, 4 
B)  4, 3, 2, 1 
C)  1, 3, 2, 4 
D)  4, 2, 3, 1 
E)  3, 1, 2, 4 C

Question 2

A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 * 10-3 kg∙m2 is suspended from the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other. The rope does not slip on the pulley. When the velocity of the heavier block is 2.0 m/s the total kinetic energy of the pulley and blocks is:

Accepted Answer

A)  2.0 J 
B)  12 J 
C)  14 J 
D)  22 J 
E)  28 J 
A)  2.0 J 
B)  12 J 
C)  14 J 
D)  22 J 
E)  28 J D

Question 3

A radian is about:

Accepted Answer

A)  25$\degree$ 
B)  37$\degree$ 
C)  45$\degree$ 
D)  57$\degree$ 
E)  90$\degree$ 
A)  25$\degree$ 
B)  37$\degree$ 
C)  45$\degree$ 
D)  57$\degree$ 
E)  90$\degree$ D

Question 4

A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A horizontal force is applied perpendicularly to the end of the stick at 0 cm, as shown. A second horizontal force (not shown) is applied at the 100-cm end of the stick. If the stick does not rotate:

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

A wheel initially has an angular velocity of 18 rad/s. It has a constant angular acceleration of 2.0 rad/s2 and is slowing at first. What time elapses before its angular velocity is18 rad/s in the direction opposite to its initial angular velocity?

Accepted Answer

A)  3.0 s 
B)  6.0 s 
C)  9.0 s 
D)  18 s 
E)  36 s 
A)  3.0 s 
B)  6.0 s 
C)  9.0 s 
D)  18 s 
E)  36 s

Question 6

When a thin uniform stick of mass M and length L is pivoted about its midpoint, its rotational inertia is ML2/12. When pivoted about a parallel axis through one end, its rotational inertia is:

Accepted Answer

A)  ML2/12 
B)  ML2/6 
C)  ML2/3 
D)  7ML2/12 
E)  13ML2/12 
A)  ML2/12 
B)  ML2/6 
C)  ML2/3 
D)  7ML2/12 
E)  13ML2/12

Question 7

The meter stick shown below rotates about an axis through the point marked $\bullet$, 20 cm from one end. Five forces act on the stick: one at each end, one at the pivot point, and two 40 cm from one end, as shown. The magnitudes of the forces are all the same. Rank the forces according to the magnitudes of the torques they produce about the pivot point, least to greatest.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

A cylinder is 0.10 m in radius and 0.20 m in length. Its rotational inertia, about the cylinder axis on which it is mounted, is 0.020 kg . m2. A string is wound around the cylinder and pulled with a force of 1.0 N. The angular acceleration of the cylinder is:

Accepted Answer

A)  2.5 rad/s2 
B)  5.0 rad/s2 
C)  10 rad/s2 
D)  15 rad/s2 
E)  20 rad/s2 
A)  2.5 rad/s2 
B)  5.0 rad/s2 
C)  10 rad/s2 
D)  15 rad/s2 
E)  20 rad/s2

Question 9

A disk with a rotational inertia of 5.0 kg.m2 and a radius of 0.25 m rotates on a frictionless fixed axis perpendicular to the disk and through its center. A force of 8.0 N is applied tangentially to the rim. If the disk starts at rest, then after it has turned through half a revolution its angular velocity is:

Accepted Answer

A)  0.57 rad/s 
B)  0.64 rad/s 
C)  0.80 rad/s 
D)  1.6 rad/s 
E)  3.2 rad/s 
A)  0.57 rad/s 
B)  0.64 rad/s 
C)  0.80 rad/s 
D)  1.6 rad/s 
E)  3.2 rad/s

Question 10

A flywheel rotating at 12 rev/s is brought to rest in 6 s. The magnitude of the average angular acceleration of the wheel during this process is:

Accepted Answer

A)  1/ $\pi$ rad/s2 
B)  2 rad/s2 
C)  4 rad/s2 
D)  4 $\pi$ rad/s2 
E)  72 rad/s2 
A)  1/ $\pi$ rad/s2 
B)  2 rad/s2 
C)  4 rad/s2 
D)  4 $\pi$ rad/s2 
E)  72 rad/s2

Question 11

A circular saw is powered by a motor. When the saw is used to cut wood, the wood exerts a torque of 0.80 N∙m on the saw blade. If the blade rotates with a constant angular velocity of 20 rad/s the work done on the blade by the motor in 1.0 min is:

Accepted Answer

A)  0 J 
B)  480 J 
C)  960 J 
D)  1500 J 
E)  1800 J 
A)  0 J 
B)  480 J 
C)  960 J 
D)  1500 J 
E)  1800 J

Question 12

The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4 if:

Accepted Answer

A)  the magnitudes of the angular velocity and the angular acceleration are each multiplied by a factor of 4 
B)  the magnitude of the angular velocity is multiplied by a factor of 4 and the angular acceleration is not changed 
C)  the magnitudes of the angular velocity and the angular acceleration are each multiplied by a factor of 2 
D)  the magnitude of the angular velocity is multiplied by a factor of 2 and the angular acceleration is not changed 
E)  the magnitude of the angular velocity is multiplied by a factor of 2 and the magnitude of the angular acceleration is multiplied by a factor of 4 
A)  the magnitudes of the angular velocity and the angular acceleration are each multiplied by a factor of 4 
B)  the magnitude of the angular velocity is multiplied by a factor of 4 and the angular acceleration is not changed 
C)  the magnitudes of the angular velocity and the angular acceleration are each multiplied by a factor of 2 
D)  the magnitude of the angular velocity is multiplied by a factor of 2 and the angular acceleration is not changed 
E)  the magnitude of the angular velocity is multiplied by a factor of 2 and the magnitude of the angular acceleration is multiplied by a factor of 4

Question 13

A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. The time it takes to make 10 revolutions is:

Accepted Answer

A)  0.50 s 
B)  0.71 s 
C)  2.2 s 
D)  2.8 s 
E)  5.6 s 
A)  0.50 s 
B)  0.71 s 
C)  2.2 s 
D)  2.8 s 
E)  5.6 s

Question 14

A certain wheel has a rotational inertia of 12 kg∙m2. As it turns through 5.0 rev its angular velocity increases from 5.0 rad/s to 6.0 rad/s. If the net torque is constant its value is:

Accepted Answer

A)  0.015 N∙m 
B)  0.18 N∙m 
C)  0.57 N∙m 
D)  2.1 N∙m 
E)  13 N∙m 
A)  0.015 N∙m 
B)  0.18 N∙m 
C)  0.57 N∙m 
D)  2.1 N∙m 
E)  13 N∙m

Question 15

The rotational inertia of a wheel about its axle does not depend upon its:

Accepted Answer

A)  diameter 
B)  mass 
C)  distribution of mass 
D)  speed of rotation 
E)  material composition 
A)  diameter 
B)  mass 
C)  distribution of mass 
D)  speed of rotation 
E)  material composition

Question 16

Three balls, with masses of 3M, 2M, and M, are fastened to a massless rod of length L as shown. The rotational inertia about the left end of the rod is:

Accepted Answer

A)  ML2/2 
B)  ML2 
C)  3ML2/2 
D)  6ML2 
E)  3ML2 
A)  ML2/2 
B)  ML2 
C)  3ML2/2 
D)  6ML2 
E)  3ML2

Question 17

A wheel starts from rest and has an angular acceleration that is given by$\alpha$(t) = (6.0 rad/s4)t2.  After it has turned through 10 rev its angular velocity is:

Accepted Answer

A)  63 rad/s 
B)  75 rad/s 
C)  89 rad/s 
D)  130 rad/s 
E)  210 rad/s 
A)  63 rad/s 
B)  75 rad/s 
C)  89 rad/s 
D)  130 rad/s 
E)  210 rad/s

Question 18

One revolution is the same as:

Accepted Answer

A)  1 rad 
B)  57 rad 
C)   $\pi$/2 rad 
D)  $\pi$ rad 
E)  2 $\pi$ rad 
A)  1 rad 
B)  57 rad 
C)   $\pi$/2 rad 
D)  $\pi$ rad 
E)  2 $\pi$ rad

Question 19

The fan shown has been turned on and is slowing as it rotates clockwise. The direction of the acceleration of the point X on the fan tip could be:

Accepted Answer

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

Question 20

The angular speed of the second hand of a watch is:

Accepted Answer

A)  ( $\pi$/1800) rad/s 
B)  ( $\pi$/60) rad/s 
C)  ( $\pi$/30) rad/s 
D)  (2 $\pi$) rad/s 
E)  (60) rad/s 
A)  ( $\pi$/1800) rad/s 
B)  ( $\pi$/60) rad/s 
C)  ( $\pi$/30) rad/s 
D)  (2 $\pi$) rad/s 
E)  (60) rad/s

Exam 10: Rotation

a hoop in the x,y plane The order of increasing rotational inertia about an axis through the center of mass and parallel to the z axis is:

A radian is about:

A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A horizontal force is applied perpendicularly to the end of the stick at 0 cm, as shown. A second horizontal force (not shown) is applied at the 100-cm end of the stick. If the stick does not rotate:

A wheel initially has an angular velocity of 18 rad/s. It has a constant angular acceleration of 2.0 rad/s2 and is slowing at first. What time elapses before its angular velocity is18 rad/s in the direction opposite to its initial angular velocity?

When a thin uniform stick of mass M and length L is pivoted about its midpoint, its rotational inertia is ML2/12. When pivoted about a parallel axis through one end, its rotational inertia is:

A cylinder is 0.10 m in radius and 0.20 m in length. Its rotational inertia, about the cylinder axis on which it is mounted, is 0.020 kg . m2. A string is wound around the cylinder and pulled with a force of 1.0 N. The angular acceleration of the cylinder is:

A flywheel rotating at 12 rev/s is brought to rest in 6 s. The magnitude of the average angular acceleration of the wheel during this process is:

A circular saw is powered by a motor. When the saw is used to cut wood, the wood exerts a torque of 0.80 N∙m on the saw blade. If the blade rotates with a constant angular velocity of 20 rad/s the work done on the blade by the motor in 1.0 min is:

The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4 if:

A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. The time it takes to make 10 revolutions is:

A certain wheel has a rotational inertia of 12 kg∙m2. As it turns through 5.0 rev its angular velocity increases from 5.0 rad/s to 6.0 rad/s. If the net torque is constant its value is:

The rotational inertia of a wheel about its axle does not depend upon its:

Three balls, with masses of 3M, 2M, and M, are fastened to a massless rod of length L as shown. The rotational inertia about the left end of the rod is:

A wheel starts from rest and has an angular acceleration that is given by α\alphaα (t) = (6.0 rad/s4)t2. After it has turned through 10 rev its angular velocity is:

One revolution is the same as:

The fan shown has been turned on and is slowing as it rotates clockwise. The direction of the acceleration of the point X on the fan tip could be:

The angular speed of the second hand of a watch is:

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A wheel initially has an angular velocity of 18 rad/s. It has a constant angular acceleration of 2.0 rad/s²and is slowing at first. What time elapses before its angular velocity is18 rad/s in the direction opposite to its initial angular velocity?

When a thin uniform stick of mass M and length L is pivoted about its midpoint, its rotational inertia is ML²/12. When pivoted about a parallel axis through one end, its rotational inertia is:

A cylinder is 0.10 m in radius and 0.20 m in length. Its rotational inertia, about the cylinder axis on which it is mounted, is 0.020 kg . m². A string is wound around the cylinder and pulled with a force of 1.0 N. The angular acceleration of the cylinder is:

A wheel starts from rest and has an angular acceleration of 4.0 rad/s². The time it takes to make 10 revolutions is:

A certain wheel has a rotational inertia of 12 kg∙m². As it turns through 5.0 rev its angular velocity increases from 5.0 rad/s to 6.0 rad/s. If the net torque is constant its value is:

A wheel starts from rest and has an angular acceleration that is given by $\alpha$ (t) = (6.0 rad/s⁴)t^2. After it has turned through 10 rev its angular velocity is: