Question 1

A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. When it has made 10 rev its angular velocity is:

Accepted Answer

A)  16 rad/s 
B)  22 rad/s 
C)  32 rad/s 
D)  250 rad/s 
E)  500 rad/s 
A)  16 rad/s 
B)  22 rad/s 
C)  32 rad/s 
D)  250 rad/s 
E)  500 rad/s

Question 2

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 3

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 4

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 5

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 6

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 7

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 8

V = I$\alpha$for an object rotating about a fixed axis, where  $ \tau $ is the net torque acting on it, I is its rotational inertia, and $\alpha$is its angular acceleration. This expression:

Accepted Answer

A)  is the definition of torque 
B)  is the definition of rotational inertia 
C)  is the definition of angular acceleration 
D)  follows directly from Newton's second law 
E)  depends on a principle of physics that is unrelated to Newton's second law 
A)  is the definition of torque 
B)  is the definition of rotational inertia 
C)  is the definition of angular acceleration 
D)  follows directly from Newton's second law 
E)  depends on a principle of physics that is unrelated to Newton's second law

Question 9

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)  zero 
B)  1 ras/s 
C)    $\pi$  ras/s 
D)    ras/s 
E)  2  $\pi$  ras/s 
A)  zero 
B)  1 ras/s 
C)    $\pi$  ras/s 
D)    ras/s 
E)  2  $\pi$  ras/s

Question 10

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

Accepted Answer

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

Question 11

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 12

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 13

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 14

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 15

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 16

An 8.0-cm radius disk with a rotational inertia of 0.12 kg .0 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 17

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 18

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 19

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 20

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

Exam 10: Rotation

A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. When it has made 10 rev its angular velocity is:

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:

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

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:

If a wheel turns with constant angular speed then:

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 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:

V = I α\alphaα for an object rotating about a fixed axis, where τ \tau τ is the net torque acting on it, I is its rotational inertia, and α\alphaα is its angular acceleration. This expression:

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:

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

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 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 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:

One revolution is the same as:

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 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:

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

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A wheel starts from rest and has an angular acceleration of 4.0 rad/s². When it has made 10 rev its angular velocity is:

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 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:

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:

V = I $\alpha$ for an object rotating about a fixed axis, where $\tau$ is the net torque acting on it, I is its rotational inertia, and $\alpha$ is its angular acceleration. This expression:

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 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 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:

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 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: