Question 1

Three identical balls, with masses of M, 2M, and 3M 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)  3ML2/4 
A)  ML2/2 
B)  ML2 
C)  3ML2/2 
D)  6ML2 
E)  3ML2/4

Question 2

String is wrapped around the periphery of a 5.0-cm radius cylinder, free to rotate on its axis. The string is pulled straight out at a constant rate of 10 cm/s and does not slip on the cylinder. As each small segment of string leaves the cylinder, its acceleration changes by:

Accepted Answer

A)  0 
B)  0.010 m/s2 
C)  0.020 m/s2 
D)  0.10 m/s2 
E)  0.20 m/s2 
A)  0 
B)  0.010 m/s2 
C)  0.020 m/s2 
D)  0.10 m/s2 
E)  0.20 m/s2

Question 3

A wheel of diameter 3.0 cm has a 4.0 m cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of 2 rad/s2. The cord will unwind in:

Accepted Answer

A)  0.82 s 
B)  2.0 s 
C)  8.0 s 
D)  16 s 
E)  130 s 
A)  0.82 s 
B)  2.0 s 
C)  8.0 s 
D)  16 s 
E)  130 s

Question 4

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

Accepted Answer

A)  (60/ $\pi$) m/s 
B)  (1800/ $\pi$) m/s 
C)  ( $\pi$) m/s 
D)  ( $\pi$/1800) m/s 
E)  ( $\pi$/60) m/s 
A)  (60/ $\pi$) m/s 
B)  (1800/ $\pi$) m/s 
C)  ( $\pi$) m/s 
D)  ( $\pi$/1800) m/s 
E)  ( $\pi$/60) m/s

Question 5

A flywheel is initially roatating at 20 rad/s and has a constant angular acceleration. After 9.0 s it has rotated through 450 rad. Its angular acceleration is:

Accepted Answer

A)  3.3 rad/s 
B)  4.4 rad/s 
C)  5.6 rad/s 
D)  6.7 rad/s 
E)  11 rad/s 
A)  3.3 rad/s 
B)  4.4 rad/s 
C)  5.6 rad/s 
D)  6.7 rad/s 
E)  11 rad/s

Question 6

An 8.0-cm radius disk with a rotational inertia of 0.12 kg . m2 is free to rotate on a horizontal axis. A string is fastened to the surface of the disk and a 10-kg mass hangs from the other end. The mass is raised by using a crank to apply a 9.0-N.m torque to the disk. The acceleration of the mass is:

Accepted Answer

A)  0.50 m/s2 
B)  1.7 m/s2 
C)  6.2 m/s2 
D)  12 m/s2 
E)  20 m/s2 
A)  0.50 m/s2 
B)  1.7 m/s2 
C)  6.2 m/s2 
D)  12 m/s2 
E)  20 m/s2

Question 7

A flywheel of diameter 1.2 m has a constant angular acceleration of 5.0 rad/s2. The tangential acceleration of a point on its rim is:

Accepted Answer

A)  5.0 rad/s2 
B)  3.0 m/s2 
C)  5.0 m/s2 
D)  6.0 m/s2 
E)  12 m/s2 
A)  5.0 rad/s2 
B)  3.0 m/s2 
C)  5.0 m/s2 
D)  6.0 m/s2 
E)  12 m/s2

Question 8

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 9

A wheel initially has an angular velocity of 36 rad/s but after 6.0s its angular velocity is 24 rad/s. If its angular acceleration is constant the value is:

Accepted Answer

A)  2.0 rad/s2 
B)  -2.0 rad/s2 
C)  3.0 rad/s2 
D)  -3.0 rad/s2 
E)  6.0 rad/s2 
A)  2.0 rad/s2 
B)  -2.0 rad/s2 
C)  3.0 rad/s2 
D)  -3.0 rad/s2 
E)  6.0 rad/s2

Question 10

A 16 kg block is attached to a cord that is wrapped around the rim of a flywheel of diameter 0.40 m and hangs vertically, as shown. The rotational inertia of the flywheel is 0.50 kg . m2. When the block is released and the cord unwinds, the acceleration of the block is:

Accepted Answer

A)  0.15 g 
B)  0.56 g 
C)  0.84 g 
D)  g 
E)  1.3 g 
A)  0.15 g 
B)  0.56 g 
C)  0.84 g 
D)  g 
E)  1.3 g

Question 11

A wheel starts from rest and has an angular acceleration that is given by $\alpha$(t) = 6rad/s4)t2. The angle through which it turns in time t is given by:

Accepted Answer

A)  [(1/8)t4] rad 
B)  [(1/4)t4] rad 
C)  [(1/2)t4] rad 
D)  (t4) rad 
E)  12 rad 
A)  [(1/8)t4] rad 
B)  [(1/4)t4] rad 
C)  [(1/2)t4] rad 
D)  (t4) rad 
E)  12 rad

Question 12

A small disk of radius R1 is fastened coaxially to a larger disk of radius R2. The combination is free to rotate on a fixed axle, which is perpendicular to a horizontal frictionless table top, as shown in the overhead veiw below. The rotational inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force   as shown. The tension in the string pulling the block is:

Accepted Answer

A)  R1F/R2 
B)  mR1R2F/(I - mR22) 
C)  mR1R2F/(I + mR22) 
D)  mR1R2F/(I - mR1R 2) 
E)  mR1R2F/(I + mR1R 2) 
A)  R1F/R2 
B)  mR1R2F/(I - mR22) 
C)  mR1R2F/(I + mR22) 
D)  mR1R2F/(I - mR1R 2) 
E)  mR1R2F/(I + mR1R 2)

Question 13

The rotational inertia of a thin cylindrical shell of mass M, radius R, and length L about its central axis (X - X') is:

Accepted Answer

A)  MR2/2 
B)  ML2/2 
C)  ML2 
D)  MR2 
E)  none of these 
A)  MR2/2 
B)  ML2/2 
C)  ML2 
D)  MR2 
E)  none of these

Question 14

For a wheel spinning with constant angular acceleration on an axis through its center, the ratio of the speed of a point on the rim to the speed of a point halfway between the center and the rim is:

Accepted Answer

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

Question 15

A phonograph turntable, initially rotating at 0.75 rev/s, slows down and stops in 30 s. The magnitude of its average angular acceleration in rad/s2 for this process is:

Accepted Answer

A)  1.5 
B)  1.5 $\pi$ 
C)   $\pi$/40 
D)   $\pi$/20 
E)  0.75 
A)  1.5 
B)  1.5 $\pi$ 
C)   $\pi$/40 
D)   $\pi$/20 
E)  0.75

Question 16

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 17

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

Question 18

A cylinder is 0.10 m in radius and 0.20 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 19

If the angular velocity vector of a spinning body points out of the page then, when viewed from above the page, the body is spinning:

Accepted Answer

A)  clockwise about an axis that is perpendicular to the page 
B)  counterclockwise about an axis that is perpendicular to the page 
C)  about an axis that is parallel to the page 
D)  about an axis that is changing orientation 
E)  about an axis that is getting longer 
A)  clockwise about an axis that is perpendicular to the page 
B)  counterclockwise about an axis that is perpendicular to the page 
C)  about an axis that is parallel to the page 
D)  about an axis that is changing orientation 
E)  about an axis that is getting longer

Question 20

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)    for all orientations of   
B)    for all orientations of   
C)    for all orientations of   
D)    for some orientations of   for others 
E)    for some orientations of   for others 
A)    for all orientations of   
B)    for all orientations of   
C)    for all orientations of   
D)    for some orientations of   for others 
E)    for some orientations of   for others

Exam 10: Rotation

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

String is wrapped around the periphery of a 5.0-cm radius cylinder, free to rotate on its axis. The string is pulled straight out at a constant rate of 10 cm/s and does not slip on the cylinder. As each small segment of string leaves the cylinder, its acceleration changes by:

A wheel of diameter 3.0 cm has a 4.0 m cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of 2 rad/s2. The cord will unwind in:

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

A flywheel is initially roatating at 20 rad/s and has a constant angular acceleration. After 9.0 s it has rotated through 450 rad. Its angular acceleration is:

A flywheel of diameter 1.2 m has a constant angular acceleration of 5.0 rad/s2. The tangential acceleration of a point on its rim is:

A wheel initially has an angular velocity of 36 rad/s but after 6.0s its angular velocity is 24 rad/s. If its angular acceleration is constant the value is:

A 16 kg block is attached to a cord that is wrapped around the rim of a flywheel of diameter 0.40 m and hangs vertically, as shown. The rotational inertia of the flywheel is 0.50 kg . m2. When the block is released and the cord unwinds, the acceleration of the block is:

A wheel starts from rest and has an angular acceleration that is given by α\alphaα (t) = 6rad/s4)t2. The angle through which it turns in time t is given by:

The rotational inertia of a thin cylindrical shell of mass M, radius R, and length L about its central axis (X - X') is:

For a wheel spinning with constant angular acceleration on an axis through its center, the ratio of the speed of a point on the rim to the speed of a point halfway between the center and the rim is:

A phonograph turntable, initially rotating at 0.75 rev/s, slows down and stops in 30 s. The magnitude of its average angular acceleration in rad/s2 for this process 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 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 cylinder is 0.10 m in radius and 0.20 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:

If the angular velocity vector of a spinning body points out of the page then, when viewed from above the page, the body is spinning:

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:

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A wheel of diameter 3.0 cm has a 4.0 m cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of 2 rad/s². The cord will unwind in:

A flywheel of diameter 1.2 m has a constant angular acceleration of 5.0 rad/s². The tangential acceleration of a point on its rim is:

A 16 kg block is attached to a cord that is wrapped around the rim of a flywheel of diameter 0.40 m and hangs vertically, as shown. The rotational inertia of the flywheel is 0.50 kg . m². When the block is released and the cord unwinds, the acceleration of the block is:

A wheel starts from rest and has an angular acceleration that is given by $\alpha$ (t) = 6rad/s⁴)t^2.The angle through which it turns in time t is given by:

A phonograph turntable, initially rotating at 0.75 rev/s, slows down and stops in 30 s. The magnitude of its average angular acceleration in rad/s² for this process 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 cylinder is 0.10 m in radius and 0.20 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: