Question 1

If a wheel turning at a constant rate completes 100 revolutions in 10 s its angular speed is:

Accepted Answer

A)  0.31 rad/s 
B)  0.63 rad/s 
C)  10 rad/s 
D)  31 rad/s 
E)  63 rad/s 
A)  0.31 rad/s 
B)  0.63 rad/s 
C)  10 rad/s 
D)  31 rad/s 
E)  63 rad/s

Question 2

If a wheel is turning at 3.0 rad/s, the time it takes to complete one revolution is about:

Accepted Answer

A)  0.33 s 
B)  0.67 s 
C)  1.0 s 
D)  1.3 s 
E)  2.1 s 
A)  0.33 s 
B)  0.67 s 
C)  1.0 s 
D)  1.3 s 
E)  2.1 s

Question 3

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

Question 4

A rod is pivoted about its center. A 5-N force is applied 4 m from the pivot and another 5-N force is applied 2 m from the pivot, as shown. The magnitude of the total torque about the pivot (in N.m) is:

Accepted Answer

A)  0 
B)  5 
C)  8.7 
D)  15 
E)  26 
A)  0 
B)  5 
C)  8.7 
D)  15 
E)  26

Question 5

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 6

A flywheel rotating at 12 rev/s is brought to rest in 6 s. The magnitude of the average angular acceleration in rad/s2 of the wheel during this process is:

Accepted Answer

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

Question 7

A child, riding on a large merry-go-round, travels a distance of 3000 m in a circle of diameter 40 m. The total angle through which she revolves is:

Accepted Answer

A)  50 rad 
B)  75 rad 
C)  150 rad 
D)  314 rad 
E)  none of these 
A)  50 rad 
B)  75 rad 
C)  150 rad 
D)  314 rad 
E)  none of these

Question 8

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)  0.016 N . m 
B)  0.18 N . m 
C)  0.57 N .m 
D)  2.1 N . m 
E)  3.6 N . m 
A)  0.016 N . m 
B)  0.18 N . m 
C)  0.57 N .m 
D)  2.1 N . m 
E)  3.6 N . m

Question 9

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 10

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

Accepted Answer

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

Question 11

A particle moves in a circular path of radius 0.10 m with a constant angular speed of 5 rev/s. The acceleration of the particle is:

Accepted Answer

A)  0.10 $\pi$ m/s2 
B)  0.50 m/s2 
C)  500 $\pi$m/s2 
D)  1000 $\pi$2 m/s2 
E)  10 $\pi$2 m/s2 
A)  0.10 $\pi$ m/s2 
B)  0.50 m/s2 
C)  500 $\pi$m/s2 
D)  1000 $\pi$2 m/s2 
E)  10 $\pi$2 m/s2

Question 12

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)  4.0 J 
C)  14 J 
D)  22 J 
E)  28 J 
A)  2.0 J 
B)  4.0 J 
C)  14 J 
D)  22 J 
E)  28 J

Question 13

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 14

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

Accepted Answer

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

Question 15

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$\degree$

Question 16

A wheel initially has an angular velocity of -36 rad/s but after 6.0 s 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 17

A 0.70-kg disk with a rotational inertia given by MR2/2 is free to rotate on a fixed horizontal axis suspended from the ceiling. A string is wrapped around the disk and a 2.0-kg mass hangs from the free end. If the string does not slip then as the mass falls and the cylinder rotates the suspension holding the cylinder pulls up on the cylinder with a force of:

Accepted Answer

A)  6.9 N 
B)  9.8 N 
C)  16 N 
D)  26 N 
E)  29 N 
A)  6.9 N 
B)  9.8 N 
C)  16 N 
D)  26 N 
E)  29 N

Question 18

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. At any instant after the blocks start moving the object with the greatest kinetic energy is:

Accepted Answer

A)  the heavier block 
B)  the lighter block 
C)  the pulley 
D)  either block (the two blocks have the same kinetic energy) 
E)  none (all three objects have the same kinetic energy) 
A)  the heavier block 
B)  the lighter block 
C)  the pulley 
D)  either block (the two blocks have the same kinetic energy) 
E)  none (all three objects have the same kinetic energy)

Question 19

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 20

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

Exam 10: Rotation

If a wheel turning at a constant rate completes 100 revolutions in 10 s its angular speed is:

If a wheel is turning at 3.0 rad/s, the time it takes to complete one revolution is about:

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:

A rod is pivoted about its center. A 5-N force is applied 4 m from the pivot and another 5-N force is applied 2 m from the pivot, as shown. The magnitude of the total torque about the pivot (in N.m) is:

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 flywheel rotating at 12 rev/s is brought to rest in 6 s. The magnitude of the average angular acceleration in rad/s2 of the wheel during this process is:

A child, riding on a large merry-go-round, travels a distance of 3000 m in a circle of diameter 40 m. The total angle through which she revolves 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 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:

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

A particle moves in a circular path of radius 0.10 m with a constant angular speed of 5 rev/s. The acceleration of the particle 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:

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

A radian is about:

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

If a wheel turns with constant angular speed then:

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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:

A flywheel rotating at 12 rev/s is brought to rest in 6 s. The magnitude of the average angular acceleration in rad/s² of the wheel during this process 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 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:

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: