Question 1

Three balls, with masses of 3M, 2M, and M, are fastened to a massless rod of length L as shown.The rotational inertia about the left end of the rod is:

Accepted Answer

A) ML2/2 
B) ML2 
C) 3ML2/2 
D) 6ML2 
E) 3ML2 
A) ML2/2 
B) ML2 
C) 3ML2/2 
D) 6ML2 
E) 3ML2

Question 2

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 3

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

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

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 angular velocity at t = 3 s is:

Accepted Answer

A) −11 rad/s 
B) −3.7 rad/s 
C) 1.0 rad/s 
D) 3.7 rad/s 
E) 11 rad/s 
A) −11 rad/s 
B) −3.7 rad/s 
C) 1.0 rad/s 
D) 3.7 rad/s 
E) 11 rad/s

Question 6

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 7

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 8

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 J 
B) 480 J 
C) 960 J 
D) 1500 J 
E) 1800 J 
A) 0 J 
B) 480 J 
C) 960 J 
D) 1500 J 
E) 1800 J

Question 9

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 10

The torque exerted on an object can be written as   .Here,   :

Accepted Answer

A) is the radius of the object. 
B) is a vector pointing from the axis of rotation to the point where the force is applied. 
C) is always perpendicular to   . 
D) is a vector pointing from the point where the force is applied to the axis of rotation. 
E) points along the axis of rotation. 
A) is the radius of the object. 
B) is a vector pointing from the axis of rotation to the point where the force is applied. 
C) is always perpendicular to   . 
D) is a vector pointing from the point where the force is applied to the axis of rotation. 
E) points along the axis of rotation.

Question 11

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 = 45.0°, θ2= −45° 
B) θ1 = 45°, θ2= 15° 
C) θ1 = 45°, θ2= −45° 
D) θ1 = 135°, θ2= −135° 
E) θ1 = −135°, θ2= 135° 
A) θ1 = 45.0°, θ2= −45° 
B) θ1 = 45°, θ2= 15° 
C) θ1 = 45°, θ2= −45° 
D) θ1 = 135°, θ2= −135° 
E) θ1 = −135°, θ2= 135°

Question 12

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 13

A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5)MR2.A light string of length 2.5 R is attached to the surface and used to suspend the sphere from the ceiling.Its rotational inertia about the point of attachment at the ceiling is:

Accepted Answer

A) (2/5)MR2 
B) 9MR2 
C) 16MR2 
D) 47/5MR2 
E) (82/5)MR2 
A) (2/5)MR2 
B) 9MR2 
C) 16MR2 
D) 47/5MR2 
E) (82/5)MR2

Question 14

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 15

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 16

An 8.0-cm radius disk with a rotational inertia of 0.12 kg.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) 3.9 m/s2 
C) 6.0 m/s2 
D) 12 m/s2 
E) 20 m/s2 
A) 0.50 m/s2 
B) 3.9 m/s2 
C) 6.0 m/s2 
D) 12 m/s2 
E) 20 m/s2

Question 17

One revolution per minute is about:

Accepted Answer

A) 0.0524 rad/s 
B) 0.105 rad/s 
C) 0.95 rad/s 
D) 1.57 rad/s 
E) 6.28 rad/s 
A) 0.0524 rad/s 
B) 0.105 rad/s 
C) 0.95 rad/s 
D) 1.57 rad/s 
E) 6.28 rad/s

Question 18

Ten seconds after an electric fan is turned on, the fan rotates at 300 rev/min.Its average angular acceleration is:

Accepted Answer

A) 3.14 rad/s2 
B) 30 rad/s2 
C) 30 rev/s2 
D) 50 rev/min2 
E) 1800 rev/s2 
A) 3.14 rad/s2 
B) 30 rad/s2 
C) 30 rev/s2 
D) 50 rev/min2 
E) 1800 rev/s2

Question 19

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

Accepted Answer

A) 1/$\pi$ rad/s2 
B) 2 rad/s2 
C) 4 rad/s2 
D) 4$\pi$rad/s2 
E) 72 rad/s2 
A) 1/$\pi$ rad/s2 
B) 2 rad/s2 
C) 4 rad/s2 
D) 4$\pi$rad/s2 
E) 72 rad/s2

Question 20

A constant torque of 260 N∙m acts on a flywheel.If the flywheel makes 25 complete revolutions in 2 minutes, what is the power exerted by the torque?

Accepted Answer

A) 54 W 
B) 200 W 
C) 340 W 
D) 3.3 x 103 W 
E) 2.0 x 104 W 
A) 54 W 
B) 200 W 
C) 340 W 
D) 3.3 x 103 W 
E) 2.0 x 104 W

Exam 10: Rotation

Three balls, with masses of 3M, 2M, and M, are fastened to a massless rod of length L as shown.The rotational inertia about the left end of the rod is:

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:

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:

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:

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 angular velocity at t = 3 s 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:

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:

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:

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

The torque exerted on an object can be written as .Here, :

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 solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5)MR2.A light string of length 2.5 R is attached to the surface and used to suspend the sphere from the ceiling.Its rotational inertia about the point of attachment at the ceiling 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 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:

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

One revolution per minute is about:

Ten seconds after an electric fan is turned on, the fan rotates at 300 rev/min.Its average angular acceleration is:

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

A constant torque of 260 N∙m acts on a flywheel.If the flywheel makes 25 complete revolutions in 2 minutes, what is the power exerted by the torque?

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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:

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 angular velocity at t = 3 s 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:

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 solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5)MR².A light string of length 2.5 R is attached to the surface and used to suspend the sphere from the ceiling.Its rotational inertia about the point of attachment at the ceiling 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 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:

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