Question 1

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation (right). If you release the hanging blocks simultaneously from rest, and call tL the time taken by the block on the left and tR the time taken by the block on the right to reach the bottom, respectively, then

Accepted Answer

A)   tL > tR.
B)   tL = tR.
C)   tL R. A

Question 2

Two forces produce equal torques on a door about the door hinge. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force has a greater magnitude?

Accepted Answer

A)   the first force (at the midpoint) 
B)   the second force (at the doorknob) 
C)   The two forces are equal. A

Question 3

A triatomic molecule is oriented as follows along the x-axis: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia of this molecule about the y-axis?

Accepted Answer

A)   2ma2
B)   3ma2
C)   12ma2
D)   14ma2 D

Question 4

A child is riding a merry-go-round that has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/s2. The child is standing 4.65 m from the center of the merry-go-round. What is the magnitude of the linear acceleration of the child?

Accepted Answer

A)   8.05 m/s2
B)   7.27 m/s2
C)   2.58 m/s2
D)   3.46 m/s2
E)   4.10 m/s2

Question 5

How long does it take for a rotating object to speed up from 15.0 rad/s to 33.3 rad/s if it has a uniform angular acceleration of 3.45 rad/s2?

Accepted Answer

A)   4.35 s
B)   5.30 s
C)   9.57 s
D)   10.6 s
E)   63.1 s

Question 6

A uniform rod is 2.0 m long. It is hinged to a wall at its left end, and held in a horizontal position at its right end by a vertical very light string, as shown in the figure. What is the angular acceleration of the rod at the moment after the string is released if there is no friction in the hinge?

Accepted Answer

A)   15 rad/s2
B)   3.3 rad/s2
C)   7.4 rad/s2
D)   11 rad/s2
E)   It cannot be calculated without knowing the mass of the rod.

Question 7

An electrical motor spins at a constant $2695.0 \mathrm { rpm } .$ If the rotor radius is $7.165 \mathrm {~cm}$ what is the linear acceleration of the edge of the rotor?

Accepted Answer

A)   5707 m/s2
B)   281.6 m/s2
C)   572,400 m/s2
D)   28.20 m/s2

Question 8

A wheel of diameter 0.70 m rolls on the floor without slipping. A point at the top of the wheel moves with a speed 2.0 m/s relative to the floor.
(a) At what speed is the central axis of the wheel moving relative to the floor?
(b) What is the angular speed of the wheel?

Accepted Answer

The answer of A wheel of diameter 0.70 m rolls...

Question 9

A 350-g air track cart on a horizontal air track is attached to a string that goes over a frictionless pulley with a moment of inertia of 6.00 × 10^-6 kg ∙ m²and a radius of 1.35 cm. If the string is pulled vertically downward by a force of 2.50 N, (a) what is the magnitude of the acceleration of the cart, and (b) what is the tension in the horizontal string between the pulley and the cart?

Accepted Answer

The answer of A 350-g air track cart on a...

Question 10

A 1.53-kg bucket hangs on a rope wrapped around a pulley of mass 7.07 kg and radius 66 cm. This pulley is frictionless in its axle, and has the shape of a solid uniform disk. After the bucket has been released, (a) what is the angular acceleration of the pulley, and (b) what is the acceleration of the bucket?

Accepted Answer

The answer of A 1.53-kg bucket hangs on a rope...

Question 11

An old 78 rpm record rotates through an angle of 320° as it slows down uniformly from 78.0 rpm to 22.8 rpm. What is the magnitude of the angular acceleration of the record?

Accepted Answer

A)   2.34 rad/s2
B)   5.46 rad/s2
C)   6.50 rad/s2
D)   8.35 rad/s2
E)   10.9 rad/s2

Question 12

A man in a gym is holding an 8.0-kg weight at arm's length, a distance of 0.55 m from his shoulder joint. What is the torque about his shoulder joint due to the weight if his arm is held at 30° below the horizontal?

Accepted Answer

A)   22 N ∙ m
B)   2.2 N ∙ m
C)   4.4 N ∙ m
D)   13 N ∙ m
E)   37 N ∙ m

Question 13

A string is wound tightly around a fixed pulley having a radius of 5.0 cm. As the string is pulled, the pulley rotates without any slipping of the string. What is the angular speed of the pulley when the string is moving at 5.0 m/s?

Accepted Answer

A)   100 rad/s
B)   50 rad/s
C)   25 rad/s
D)   20 rad/s
E)   10 rad/s

Question 14

The figure shows a person's foot. In that figure, the Achilles tendon exerts a force of magnitude F = 720 N. What is the magnitude of the torque that this force produces about the ankle joint?

Accepted Answer

A)   12 N ∙ m
B)   16 N ∙ m
C)   21 N ∙ m
D)   26 N ∙ m
E)   36 N ∙ m

Question 15

A particular motor can provide a maximum torque of 110 N ? m. Assuming that all of this torque is used to accelerate a solid, uniform, cylindrical flywheel of mass 10.0 kg and radius 3.00 m, how long will it take for the flywheel to accelerate from rest to $8.13 \mathrm { rad } / \mathrm { s } ?$

Accepted Answer

A)   3.33 s
B)   2.83 s
C)   4.03 s
D)   4.36 s

Question 16

The lug nuts on a car wheel require tightening to a torque of 90 N ∙ m. If a 30-cm long wrench is used, what is the magnitude of the minimum force required using the wrench?

Accepted Answer

A)   300 N
B)   150 N
C)   30 N
D)   15 N

Question 17

When a rigid object rotates about a fixed axis, what is true about all the points in the object? (There could be more than one correct choice.)

Accepted Answer

A)   They all have the same angular speed.
B)   They all have the same tangential speed.
C)   They all have the same angular acceleration.
D)   They all have the same tangential acceleration.
E)   They all have the same radial acceleration.

Question 18

A uniform, solid, 100-kg cylinder with a diameter of 1.0 m is mounted so it is free to rotate about fixed, horizontal, frictionless axis that passes through the centers of its circular ends. A 10-kg block is hung from a very light thin cord wrapped around the cylinder's circumference. When the block is released, the cord unwinds and the block accelerates downward, as shown in the figure. What is the acceleration of the block?

Accepted Answer

The answer of A uniform, solid, 100-kg cylinder with a...

Question 19

The L-shaped object shown in the figure consists of three small masses connected by thin uniform rods, each rod of mass 3.00 kg. Assume that the masses shown are accurate to three significant figures. What is the moment of inertia of this object (a) about the x-axis, and (b) about the y-axis?

Accepted Answer

The answer of The L-shaped object shown in the figure...

Question 20

A 95-N force exerted at the end of a 0.32-m long torque wrench produces a torque of 15 N ∙ m. What is the angle (less than 90°) between the wrench handle and the direction of the applied force?

Accepted Answer

A)   30°
B)   24°
C)   36°
D)   42°

Exam 7: Rotational Motion

Two forces produce equal torques on a door about the door hinge. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force has a greater magnitude?

A triatomic molecule is oriented as follows along the x-axis: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia of this molecule about the y-axis?

A child is riding a merry-go-round that has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/s². The child is standing 4.65 m from the center of the merry-go-round. What is the magnitude of the linear acceleration of the child?

How long does it take for a rotating object to speed up from 15.0 rad/s to 33.3 rad/s if it has a uniform angular acceleration of 3.45 rad/s²?

An electrical motor spins at a constant $2695.0 \mathrm { rpm } .$ If the rotor radius is $7.165 \mathrm {~cm}$ what is the linear acceleration of the edge of the rotor?

A wheel of diameter 0.70 m rolls on the floor without slipping. A point at the top of the wheel moves with a speed 2.0 m/s relative to the floor. (a) At what speed is the central axis of the wheel moving relative to the floor? (b) What is the angular speed of the wheel?

An old 78 rpm record rotates through an angle of 320° as it slows down uniformly from 78.0 rpm to 22.8 rpm. What is the magnitude of the angular acceleration of the record?

A man in a gym is holding an 8.0-kg weight at arm's length, a distance of 0.55 m from his shoulder joint. What is the torque about his shoulder joint due to the weight if his arm is held at 30° below the horizontal?

A string is wound tightly around a fixed pulley having a radius of 5.0 cm. As the string is pulled, the pulley rotates without any slipping of the string. What is the angular speed of the pulley when the string is moving at 5.0 m/s?

The figure shows a person's foot. In that figure, the Achilles tendon exerts a force of magnitude F = 720 N. What is the magnitude of the torque that this force produces about the ankle joint?

A particular motor can provide a maximum torque of 110 N ? m. Assuming that all of this torque is used to accelerate a solid, uniform, cylindrical flywheel of mass 10.0 kg and radius 3.00 m, how long will it take for the flywheel to accelerate from rest to $8.13 \mathrm { rad } / \mathrm { s } ?$

The lug nuts on a car wheel require tightening to a torque of 90 N ∙ m. If a 30-cm long wrench is used, what is the magnitude of the minimum force required using the wrench?

When a rigid object rotates about a fixed axis, what is true about all the points in the object? (There could be more than one correct choice.)

The L-shaped object shown in the figure consists of three small masses connected by thin uniform rods, each rod of mass 3.00 kg. Assume that the masses shown are accurate to three significant figures. What is the moment of inertia of this object (a) about the x-axis, and (b) about the y-axis?

A 95-N force exerted at the end of a 0.32-m long torque wrench produces a torque of 15 N ∙ m. What is the angle (less than 90°) between the wrench handle and the direction of the applied force?

Exam 7: Rotational Motion

Two forces produce equal torques on a door about the door hinge. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force has a greater magnitude?

A triatomic molecule is oriented as follows along the x-axis: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia of this molecule about the y-axis?

A child is riding a merry-go-round that has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/s2. The child is standing 4.65 m from the center of the merry-go-round. What is the magnitude of the linear acceleration of the child?

How long does it take for a rotating object to speed up from 15.0 rad/s to 33.3 rad/s if it has a uniform angular acceleration of 3.45 rad/s2?

An electrical motor spins at a constant 2695.0rpm.2695.0 \mathrm { rpm } .2695.0rpm. If the rotor radius is 7.165 cm7.165 \mathrm {~cm}7.165 cm what is the linear acceleration of the edge of the rotor?

A wheel of diameter 0.70 m rolls on the floor without slipping. A point at the top of the wheel moves with a speed 2.0 m/s relative to the floor. (a) At what speed is the central axis of the wheel moving relative to the floor? (b) What is the angular speed of the wheel?

An old 78 rpm record rotates through an angle of 320° as it slows down uniformly from 78.0 rpm to 22.8 rpm. What is the magnitude of the angular acceleration of the record?

A man in a gym is holding an 8.0-kg weight at arm's length, a distance of 0.55 m from his shoulder joint. What is the torque about his shoulder joint due to the weight if his arm is held at 30° below the horizontal?

A string is wound tightly around a fixed pulley having a radius of 5.0 cm. As the string is pulled, the pulley rotates without any slipping of the string. What is the angular speed of the pulley when the string is moving at 5.0 m/s?

The figure shows a person's foot. In that figure, the Achilles tendon exerts a force of magnitude F = 720 N. What is the magnitude of the torque that this force produces about the ankle joint?

The lug nuts on a car wheel require tightening to a torque of 90 N ∙ m. If a 30-cm long wrench is used, what is the magnitude of the minimum force required using the wrench?

When a rigid object rotates about a fixed axis, what is true about all the points in the object? (There could be more than one correct choice.)

The L-shaped object shown in the figure consists of three small masses connected by thin uniform rods, each rod of mass 3.00 kg. Assume that the masses shown are accurate to three significant figures. What is the moment of inertia of this object (a) about the x-axis, and (b) about the y-axis?

A 95-N force exerted at the end of a 0.32-m long torque wrench produces a torque of 15 N ∙ m. What is the angle (less than 90°) between the wrench handle and the direction of the applied force?

A child is riding a merry-go-round that has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/s². The child is standing 4.65 m from the center of the merry-go-round. What is the magnitude of the linear acceleration of the child?

How long does it take for a rotating object to speed up from 15.0 rad/s to 33.3 rad/s if it has a uniform angular acceleration of 3.45 rad/s²?

An electrical motor spins at a constant $2695.0 \mathrm { rpm } .$ If the rotor radius is $7.165 \mathrm {~cm}$ what is the linear acceleration of the edge of the rotor?