Question 1

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)  0.32 kg.m2 
B)  0.54 kg.m2 
C)  0.70 kg.m2 
D)  0.86 kg.m2 
E)  1.0 kg.m2 
A)  0.32 kg.m2 
B)  0.54 kg.m2 
C)  0.70 kg.m2 
D)  0.86 kg.m2 
E)  1.0 kg.m2

Question 2

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

Question 3

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 4

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 5

This graph shows the angular velocity of a turntable as a function of time. What is its average angular acceleration between t = 2 s and t = 4 s?

Accepted Answer

A)  −10 rad/s2  
B)  −5 rad/s2 
C)  0 rad/s2 
D)  5 rad/s2 
E)  10 rad/s2 
A)  −10 rad/s2  
B)  −5 rad/s2 
C)  0 rad/s2 
D)  5 rad/s2 
E)  10 rad/s2

Question 6

Consider four objects, each having the same mass and the same radius:
1. a solid sphere 
2. a hollow sphere 
3. a flat disk in the x,y plane 
4. 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 7

This graph shows the angular velocity of a turntable as a function of time. What is its angular acceleration at t = 3.5 s?

Accepted Answer

A)  −10 rad/s2  
B)  −5 rad/s2 
C)  0 rad/s2 
D)  5 rad/s2 
E)  10 rad/s2 
A)  −10 rad/s2  
B)  −5 rad/s2 
C)  0 rad/s2 
D)  5 rad/s2 
E)  10 rad/s2

Question 8

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 9

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 10

An object rotates from θ1 to θ2 through an angle that is less than 2π radians. Which of the following represents its angular displacement?

Accepted Answer

A)  θ1 
B)  θ2 
C)  θ1 - θ2 
D)  θ2 - θ1 
E)  θ1 + θ2 
A)  θ1 
B)  θ2 
C)  θ1 - θ2 
D)  θ2 - θ1 
E)  θ1 + θ2

Question 11

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 is:

Accepted Answer

A)  0 N.m 
B)  5.0 N.m 
C)  8.7 N.m 
D)  15 N.m 
E)  26 N.m 
A)  0 N.m 
B)  5.0 N.m 
C)  8.7 N.m 
D)  15 N.m 
E)  26 N.m

Question 12

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

Accepted Answer

A)  1.5 rad/s2 
B)  1.5 $\pi$ rad/s2 
C)   $\pi$/40 rad/s2 
D)   $\pi$/20 rad/s2 
E)  0.75 rad/s2 
A)  1.5 rad/s2 
B)  1.5 $\pi$ rad/s2 
C)   $\pi$/40 rad/s2 
D)   $\pi$/20 rad/s2 
E)  0.75 rad/s2

Question 13

A block is attached to each end of a rope that passes over a pulley suspended from the ceiling. The blocks do not have the same mass. If the rope does not slip on the pulley, then at any instant after the blocks start moving, the rope:

Accepted Answer

A)  pulls on both blocks, but exerts a greater force on the heavier block 
B)  pulls on both blocks, but exerts a greater force on the lighter block 
C)  pulls on both blocks and exerts the same magnitude force on both blocks 
D)  does not pull on either block 
E)  pulls only on the lighter block 
A)  pulls on both blocks, but exerts a greater force on the heavier block 
B)  pulls on both blocks, but exerts a greater force on the lighter block 
C)  pulls on both blocks and exerts the same magnitude force on both blocks 
D)  does not pull on either block 
E)  pulls only on the lighter block

Question 14

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)  8.9 rad/s 
B)  16 rad/s 
C)  22 rad/s 
D)  32 rad/s 
E)  250 rad/s 
A)  8.9 rad/s 
B)  16 rad/s 
C)  22 rad/s 
D)  32 rad/s 
E)  250 rad/s

Question 15

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 16

The rotational inertia of a solid uniform sphere about a diameter is (2/5)MR2, where M is its mass and R is its radius. If the sphere is pivoted about an axis that is tangent to its surface, its rotational inertia is:

Accepted Answer

A)  MR2 
B)  (2/5)MR2 
C)  (3/5)MR2 
D)  (5/2)MR2 
E)  (7/5)MR2 
A)  MR2 
B)  (2/5)MR2 
C)  (3/5)MR2 
D)  (5/2)MR2 
E)  (7/5)MR2

Question 17

A uniform disk, a thin hoop, and a uniform solid sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center. Assume the hoop is connected to the rotation axis by light spokes. With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown. Rank the objects according to their angular velocities after a given time t, least to greatest.

Accepted Answer

A)  disk, hoop, sphere 
B)  disk, sphere, hoop 
C)  hoop, sphere, disk 
D)  hoop, disk, sphere 
E)  sphere, disk, hoop 
A)  disk, hoop, sphere 
B)  disk, sphere, hoop 
C)  hoop, sphere, disk 
D)  hoop, disk, sphere 
E)  sphere, disk, hoop

Question 18

An object rotates from θ1 to θ2 through an angle that is less than π radians. Which of the following results in a positive angular displacement?

Accepted Answer

A)  θ1 = 45°, θ2= −45° 
B)  θ1 = 45°, θ2= 15° 
C)  θ1 = 45°, θ2= −40° 
D)  θ1 = 135°, θ2= −135° 
E)  θ1 = −135°, θ2= 135° 
A)  θ1 = 45°, θ2= −45° 
B)  θ1 = 45°, θ2= 15° 
C)  θ1 = 45°, θ2= −40° 
D)  θ1 = 135°, θ2= −135° 
E)  θ1 = −135°, θ2= 135°

Question 19

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 mass 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 20

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

Exam 10: Rotation

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 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:

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:

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:

This graph shows the angular velocity of a turntable as a function of time. What is its average angular acceleration between t = 2 s and t = 4 s?

Consider four objects, each having the same mass and the same radius: 1. a solid sphere 2. a hollow sphere 3. a flat disk in the x,y plane 4. 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:

This graph shows the angular velocity of a turntable as a function of time. What is its angular acceleration at t = 3.5 s?

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:

An object rotates from θ1 to θ2 through an angle that is less than 2π radians. Which of the following represents its angular displacement?

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 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 for this process is:

A block is attached to each end of a rope that passes over a pulley suspended from the ceiling. The blocks do not have the same mass. If the rope does not slip on the pulley, then at any instant after the blocks start moving, the rope:

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:

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:

The rotational inertia of a solid uniform sphere about a diameter is (2/5)MR2, where M is its mass and R is its radius. If the sphere is pivoted about an axis that is tangent to its surface, its rotational inertia is:

An object rotates from θ1 to θ2 through an angle that is less than π radians. Which of the following results in a positive angular displacement?

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:

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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 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:

An object rotates from θ₁ to θ₂ through an angle that is less than 2π radians. Which of the following represents its angular displacement?

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:

The rotational inertia of a solid uniform sphere about a diameter is (2/5)MR², where M is its mass and R is its radius. If the sphere is pivoted about an axis that is tangent to its surface, its rotational inertia is:

An object rotates from θ₁ to θ₂ through an angle that is less than π radians. Which of the following results in a positive angular displacement?