Question 1

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

Accepted Answer

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

Question 2

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 
B)  480 J 
C)  960 J 
D)  1400 J 
E)  1800 J 
A)  0 
B)  480 J 
C)  960 J 
D)  1400 J 
E)  1800 J

Question 3

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 along the rotation axis. The angular acceleration of the disk is:

Accepted Answer

A)  0 
B)  0.40 rad/s2 
C)  0.60 rad/s2 
D)  1.0 rad/s2 
E)  2.5 rad/s2 
A)  0 
B)  0.40 rad/s2 
C)  0.60 rad/s2 
D)  1.0 rad/s2 
E)  2.5 rad/s2

Question 4

A small disk of radius R1 is mounted coaxially with a larger disk of radius R2. The disks are securely fastened to each other and the combination is free to rotate on a fixed axle that 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 acceleration of the block is:

Accepted Answer

A)  R1F/mR2 
B)  R1R2F/(I - mR2 2) 
C)  R1R2F/(I + mR2 2) 
D)  R1R2F/(I - mR1R 2) 
E)  R1R2F/(I + mR1R 2) 
A)  R1F/mR2 
B)  R1R2F/(I - mR2 2) 
C)  R1R2F/(I + mR2 2) 
D)  R1R2F/(I - mR1R 2) 
E)  R1R2F/(I + mR1R 2)

Question 5

Two wheels are identical but wheel B is spinning with twice the angular speed of wheel A. The ratio of the magnitued of the radical acceleration of a point on the rim of B to the magnitude of the radial acceleration of a point on the rim of A 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 6

A and B are two solid cylinders made of aluminum. Their dimensions are shown. The ratio of the rotational inertia of B to that of A about the common axis X─X' is:

Accepted Answer

A)  2 
B)  4 
C)  8 
D)  16 
E)  32 
A)  2 
B)  4 
C)  8 
D)  16 
E)  32

Question 7

The figure shows a cylinder of radius 0.7 m rotating about its axis at 10 rad/s. The speed of the point P is:

Accepted Answer

A)  7.0 m/s 
B)  14  $\pi$  rad/s 
C)  7  $\pi$ rad/s 
D)  0.70 m/s 
E)  none of these 
A)  7.0 m/s 
B)  14  $\pi$  rad/s 
C)  7  $\pi$ rad/s 
D)  0.70 m/s 
E)  none of these

Question 8

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 9

For a wheel spinning on an axis through its center, the ratio of the radial acceleration of a point on the rim to the radial acceleration 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 10

A wheel starts from rest and has an angular acceleration that is given by  $\alpha$ (t) = (6.0 rad/s4)t2. The time it takes to make 10 rev is:

Accepted Answer

A)  2.8 s 
B)  3.3 s 
C)  4.0 s 
D)  4.7 s 
E)  5.3 s 
A)  2.8 s 
B)  3.3 s 
C)  4.0 s 
D)  4.7 s 
E)  5.3 s

Question 11

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 12

To increase the rotational inertia of a solid disk about its axis without changing its mass:

Accepted Answer

A)  drill holes near the rim and put the material near the axis 
B)  drill holes near the axis and put the material near the rim 
C)  drill holes at points on a circle near the rim and put the material at points between the holes 
D)  drill holes at points on a circle near the axis and put the material at points between the holes 
E)  do none of the above (the rotational inertia cannot be changed without changing the mass) 
A)  drill holes near the rim and put the material near the axis 
B)  drill holes near the axis and put the material near the rim 
C)  drill holes at points on a circle near the rim and put the material at points between the holes 
D)  drill holes at points on a circle near the axis and put the material at points between the holes 
E)  do none of the above (the rotational inertia cannot be changed without changing the mass)

Question 13

The rotational inertia of a disk about its axis is 0.70 kg . m2. When a 2.0 kg weight is added to its rim, 0.40 m from the axis, the rotational inertia becomes:

Accepted Answer

A)  0.38 kg . m2 
B)  0.54 kg. m2 
C)  0.70 kg . m2 
D)  0.86 kg . m2 
E)  1.0 kg . m2 
A)  0.38 kg . m2 
B)  0.54 kg. m2 
C)  0.70 kg . m2 
D)  0.86 kg . m2 
E)  1.0 kg . m2

Question 14

Three identical balls are tied by light strings to the same rod and rotate around it, as shown below. Rank the balls according to their rotational inertia, least to greatest.

Accepted Answer

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

Question 15

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 16

Four identical particles, each with mass m, are arranged in the x, y plane as shown. They are connected by light sticks to form a rigid body. If m = 2.0 kg and a = 1.0 m, the rotational inertia of this array about the y-axis is:

Accepted Answer

A)  4.0 kg . m2 
B)  12 kg. m2 
C)  9.6 kg . m2 
D)  4.8 kg . m2 
E)  none of these 
A)  4.0 kg . m2 
B)  12 kg. m2 
C)  9.6 kg . m2 
D)  4.8 kg . m2 
E)  none of these

Question 17

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 18

A wheel initially has an angular velocity of 18 rad/s but it is slowing at a rate of 2.0 rad/s2. By the time it stops it will have turned through:

Accepted Answer

A)  81 rad 
B)  160 rad 
C)  245 rad 
D)  330 rad 
E)  410 rad 
A)  81 rad 
B)  160 rad 
C)  245 rad 
D)  330 rad 
E)  410 rad

Question 19

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 20

A wheel starts from rest and spins with a constant angular acceleration. As time goes on the acceleration vector for a point on the rim:

Accepted Answer

A)  decreases in magnitude and becomes more nearly tangent to the rim 
B)  decreases in magnitude and becomes more nearly radial 
C)  increases in magnitude and becomes more nearly tangent to the rim 
D)  increases in magnitude and becomes more nearly radial 
E)  increases in magnitude but retains the same angle with the tangent to the rim 
A)  decreases in magnitude and becomes more nearly tangent to the rim 
B)  decreases in magnitude and becomes more nearly radial 
C)  increases in magnitude and becomes more nearly tangent to the rim 
D)  increases in magnitude and becomes more nearly radial 
E)  increases in magnitude but retains the same angle with the tangent to the rim

Exam 10: Rotation

The angular speed of the second hand of a watch 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:

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 along the rotation axis. The angular acceleration of the disk is:

Two wheels are identical but wheel B is spinning with twice the angular speed of wheel A. The ratio of the magnitued of the radical acceleration of a point on the rim of B to the magnitude of the radial acceleration of a point on the rim of A is:

A and B are two solid cylinders made of aluminum. Their dimensions are shown. The ratio of the rotational inertia of B to that of A about the common axis X─X' is:

The figure shows a cylinder of radius 0.7 m rotating about its axis at 10 rad/s. The speed of the point P is:

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

A wheel starts from rest and has an angular acceleration that is given by α\alphaα (t) = (6.0 rad/s4)t2. The time it takes to make 10 rev 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:

To increase the rotational inertia of a solid disk about its axis without changing its mass:

The rotational inertia of a disk about its axis is 0.70 kg . m2. When a 2.0 kg weight is added to its rim, 0.40 m from the axis, the rotational inertia becomes:

Three identical balls are tied by light strings to the same rod and rotate around it, as shown below. Rank the balls according to their rotational inertia, least to greatest.

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:

Four identical particles, each with mass m, are arranged in the x, y plane as shown. They are connected by light sticks to form a rigid body. If m = 2.0 kg and a = 1.0 m, the rotational inertia of this array about the y-axis 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 wheel initially has an angular velocity of 18 rad/s but it is slowing at a rate of 2.0 rad/s2. By the time it stops it will have turned through:

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

A wheel starts from rest and spins with a constant angular acceleration. As time goes on the acceleration vector for a point on the rim:

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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 along the rotation axis. The angular acceleration of the disk is:

A wheel starts from rest and has an angular acceleration that is given by $\alpha$ (t) = (6.0 rad/s⁴)t². The time it takes to make 10 rev 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:

The rotational inertia of a disk about its axis is 0.70 kg . m². When a 2.0 kg weight is added to its rim, 0.40 m from the axis, the rotational inertia becomes:

A wheel initially has an angular velocity of 18 rad/s but it is slowing at a rate of 2.0 rad/s². By the time it stops it will have turned through: