Question 1

This graph shows the angular position of an object as a function of time. What is its average angular velocity between t = 5 s and t = 9 s?

Accepted Answer

A)  3 rad/s 
B)  −3 rad/s 
C)  12 rad/s 
D)  −12 rad/s 
E)  Need additional information. 
A)  3 rad/s 
B)  −3 rad/s 
C)  12 rad/s 
D)  −12 rad/s 
E)  Need additional information.

Question 2

A flywheel is initially rotating 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)  6.7 rad/s 
D)  11 rad/s 
E)  48 rad/s 
A)  3.3 rad/s 
B)  4.4 rad/s 
C)  6.7 rad/s 
D)  11 rad/s 
E)  48 rad/s

Question 3

A thin circular hoop of mass 1.0 kg and radius 2.0 m is rotating about an axis through its center and perpendicular to its plane. It is slowing down at the rate of 7.0 rad/s2. The net torque acting on it is:

Accepted Answer

A)  7.0 N∙m 
B)  14 N∙m 
C)  28 N∙m 
D)  44 N∙m 
E)  none of these 
A)  7.0 N∙m 
B)  14 N∙m 
C)  28 N∙m 
D)  44 N∙m 
E)  none of these

Question 4

A disk has a rotational inertia of 6.0 kg∙m2 and a constant angular acceleration of 2.0 rad/s2. If it starts from rest the work done during the first 5.0 s by the net torque acting on it is:

Accepted Answer

A)  0 J 
B)  30 J 
C)  60 J 
D)  300 J 
E)  600 J 
A)  0 J 
B)  30 J 
C)  60 J 
D)  300 J 
E)  600 J

Question 5

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

Accepted Answer

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

Question 6

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 view 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 - mR22) 
C)  R1R2F/(I + mR22) 
D)  R1R2F/(I - mR1R2) 
E)  R1R2F/(I + mR1R2) 
A)  R1F/mR2 
B)  R1R2F/(I - mR22) 
C)  R1R2F/(I + mR22) 
D)  R1R2F/(I - mR1R2) 
E)  R1R2F/(I + mR1R2)

Question 7

A disk starts from rest and rotates around a fixed axis, subject to a constant net torque. The work done by the torque during the second 5 s is ______ as the work done during the first 5 s.

Accepted Answer

A)  the same 
B)  half as much 
C)  twice as much 
D)  three times as much 
E)  four times as much 
A)  the same 
B)  half as much 
C)  twice as much 
D)  three times as much 
E)  four times as much

Question 8

If a wheel turns with constant angular speed then:

Accepted Answer

A)  each point on its rim moves with constant velocity 
B)  each point on its rim moves with constant acceleration 
C)  the wheel turns through equal angles in equal times 
D)  the angle through which the wheel turns in each second increases as time goes on 
E)  the angle through which the wheel turns in each second decreases as time goes on 
A)  each point on its rim moves with constant velocity 
B)  each point on its rim moves with constant acceleration 
C)  the wheel turns through equal angles in equal times 
D)  the angle through which the wheel turns in each second increases as time goes on 
E)  the angle through which the wheel turns in each second decreases as time goes on

Question 9

The angular velocity vector of a spinning body points out of the page. If the angular acceleration vector points into the page then:

Accepted Answer

A)  the body is slowing down 
B)  the body is speeding up 
C)  the body is starting to turn in the opposite direction 
D)  the axis of rotation is changing orientation 
E)  none of the above 
A)  the body is slowing down 
B)  the body is speeding up 
C)  the body is starting to turn in the opposite direction 
D)  the axis of rotation is changing orientation 
E)  none of the above

Question 10

For a wheel spinning on an axis through its center, the ratio of the tangential acceleration of a point on the rim to the tangential 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 11

The coordinate of an object is given as a function of time by θ = 7t - 3t2, where θ is in radians and t is in seconds. Its average velocity over the interval from t = 0 to t = 2 s is:

Accepted Answer

A)  5 rad/s 
B)  -5 rad/s 
C)  11 rad/s 
D)  -11 rad/s 
E)  1 rad/s 
A)  5 rad/s 
B)  -5 rad/s 
C)  11 rad/s 
D)  -11 rad/s 
E)  1 rad/s

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

Two wheels are identical but wheel B is spinning with twice the angular speed of wheel A. The ratio of the magnitude of the radial 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 14

Wrapping paper is being unwrapped from a 5.0-cm radius tube, free to rotate on its axis. If it is pulled at the constant rate of 10 cm/s and does not slip on the tube, the angular velocity of the tube is:

Accepted Answer

A)  2.0 rad/s 
B)  5.0 rad/s 
C)  10 rad/s 
D)  25 rad/s 
E)  50 rad/s 
A)  2.0 rad/s 
B)  5.0 rad/s 
C)  10 rad/s 
D)  25 rad/s 
E)  50 rad/s

Question 15

A wheel rotates with a constant angular acceleration of  $\pi$ rad/s2. During a certain time interval its angular displacement is  $\pi$ rad. At the end of the interval its angular velocity is 2 $\pi$ rad/s. Its angular velocity at the beginning of the interval is:

Accepted Answer

A)  0 rad/s 
B)  1 rad/s 
C)   $\pi$ rad/s 
D)  rad/s 
E)  2 $\pi$rad/s 
A)  0 rad/s 
B)  1 rad/s 
C)   $\pi$ rad/s 
D)  rad/s 
E)  2 $\pi$rad/s

Question 16

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

Question 17

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)  1.0 g 
E)  1.3 g 
A)  0.15 g 
B)  0.56 g 
C)  0.84 g 
D)  1.0 g 
E)  1.3 g

Question 18

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 19

A disk with a rotational inertia of 2.0 kg.m2 and a radius of 0.40 m rotates on a frictionless fixed axis perpendicular to the disk faces and through its center. A force of 5.0 N is applied tangentially to the rim. The angular acceleration of the disk is:

Accepted Answer

A)  0.40 rad/s2 
B)  0.60 rad/s2 
C)  1.0 rad/s2 
D)  2.5 rad/s2 
E)  10 rad/s2 
A)  0.40 rad/s2 
B)  0.60 rad/s2 
C)  1.0 rad/s2 
D)  2.5 rad/s2 
E)  10 rad/s2

Question 20

A force with a given magnitude is to be applied to a wheel. The torque can be maximized by:

Accepted Answer

A)  applying the force near the axle, radially outward from the axle 
B)  applying the force near the rim, radially outward from the axle 
C)  applying the force near the axle, parallel to a tangent to the wheel 
D)  applying the force at the rim, tangent to the rim 
E)  applying the force at the rim, at 45$\degree$ to the tangent 
A)  applying the force near the axle, radially outward from the axle 
B)  applying the force near the rim, radially outward from the axle 
C)  applying the force near the axle, parallel to a tangent to the wheel 
D)  applying the force at the rim, tangent to the rim 
E)  applying the force at the rim, at 45$\degree$ to the tangent

Exam 10: Rotation

This graph shows the angular position of an object as a function of time. What is its average angular velocity between t = 5 s and t = 9 s?

A flywheel is initially rotating 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 thin circular hoop of mass 1.0 kg and radius 2.0 m is rotating about an axis through its center and perpendicular to its plane. It is slowing down at the rate of 7.0 rad/s2. The net torque acting on it is:

A disk has a rotational inertia of 6.0 kg∙m2 and a constant angular acceleration of 2.0 rad/s2. If it starts from rest the work done during the first 5.0 s by the net torque acting on it is:

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

A disk starts from rest and rotates around a fixed axis, subject to a constant net torque. The work done by the torque during the second 5 s is ______ as the work done during the first 5 s.

If a wheel turns with constant angular speed then:

The angular velocity vector of a spinning body points out of the page. If the angular acceleration vector points into the page then:

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

The coordinate of an object is given as a function of time by θ = 7t - 3t2, where θ is in radians and t is in seconds. Its average velocity over the interval from t = 0 to t = 2 s is:

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

Two wheels are identical but wheel B is spinning with twice the angular speed of wheel A. The ratio of the magnitude of the radial 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:

Wrapping paper is being unwrapped from a 5.0-cm radius tube, free to rotate on its axis. If it is pulled at the constant rate of 10 cm/s and does not slip on the tube, the angular velocity of the tube is:

A wheel rotates with a constant angular acceleration of π\piπ rad/s2. During a certain time interval its angular displacement is π\piπ rad. At the end of the interval its angular velocity is 2 π\piπ rad/s. Its angular velocity at the beginning of the interval 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:

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:

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 disk with a rotational inertia of 2.0 kg.m2 and a radius of 0.40 m rotates on a frictionless fixed axis perpendicular to the disk faces and through its center. A force of 5.0 N is applied tangentially to the rim. The angular acceleration of the disk is:

A force with a given magnitude is to be applied to a wheel. The torque can be maximized by:

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A thin circular hoop of mass 1.0 kg and radius 2.0 m is rotating about an axis through its center and perpendicular to its plane. It is slowing down at the rate of 7.0 rad/s². The net torque acting on it is:

A disk has a rotational inertia of 6.0 kg∙m² and a constant angular acceleration of 2.0 rad/s². If it starts from rest the work done during the first 5.0 s by the net torque acting on it is:

The coordinate of an object is given as a function of time by θ = 7t - 3t², where θ is in radians and t is in seconds. Its average velocity over the interval from t = 0 to t = 2 s is:

A wheel rotates with a constant angular acceleration of $\pi$ rad/s². During a certain time intervalits angular displacement is $\pi$ rad. At the end of the interval its angular velocity is 2 $\pi$ rad/s. Its angular velocity at the beginning of the interval 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 disk with a rotational inertia of 2.0 kg.m² and a radius of 0.40 m rotates on a frictionless fixed axis perpendicular to the disk faces and through its center. A force of 5.0 N is applied tangentially to the rim. The angular acceleration of the disk is: