Question 1

A bicycle wheel has an outside diameter of 66 cm. Through what distance does a point on the rim move as the wheel rotates through an angle of 70°?

Accepted Answer

The answer of A bicycle wheel has an outside diameter...

Question 2

A machinist turns on the power on to a grinding wheel at time t = 0 s. The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of $58 \mathrm { rad } / \mathrm { s }$ The wheel is run at that angular velocity for 30 s, and then power is shut off. The wheel slows down uniformly at $1.4 \mathrm { rad } / \mathrm { s } ^ { 2 }$ until the wheel stops. What is the total number of revolutions made by the wheel in this situation?

Accepted Answer

A)  510 
B)  280 
C)  320 
D)  470 
E)  750 
A)  510 
B)  280 
C)  320 
D)  470 
E)  750

Question 3

What is the angular speed, in rad/s, of a flywheel turning at 813.0 rpm?

Accepted Answer

A)  85.14 rad/s 
B)  13.53 rad/s 
C)  63.84 rad/s 
D)  95.33 rad/s 
A)  85.14 rad/s 
B)  13.53 rad/s 
C)  63.84 rad/s 
D)  95.33 rad/s

Question 4

A chicken is running in a circular path with an angular speed of 1.52 rad/s. How long does it take the chicken to complete one revolution?

Accepted Answer

A)  4.13 s 
B)  2.07 s 
C)  118 s 
D)  4.77 s 
E)  8.26 s 
A)  4.13 s 
B)  2.07 s 
C)  118 s 
D)  4.77 s 
E)  8.26 s

Question 5

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 horizontal?

Accepted Answer

A)  0.24 N ∙ m 
B)  4.4 N ∙ m 
C)  43 N ∙ m 
D)  15 N ∙ m 
E)  0 N ∙ m 
A)  0.24 N ∙ m 
B)  4.4 N ∙ m 
C)  43 N ∙ m 
D)  15 N ∙ m 
E)  0 N ∙ m

Question 6

A machinist turns on the power to a grinding wheel at time t = 0 s. The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of $38 \mathrm { rad } / \mathrm { s }$ The wheel is run at that angular speed for 30 s and then power is shut off. The wheel slows down uniformly at $2.1 \mathrm { rad } / \mathrm { s } ^ { 2 }$ until the wheel stops. In this situation, what is the angular acceleration of the wheel between $t = 0 \mathrm {~s}$ and $t = 10 \mathrm {~s} ?$

Accepted Answer

A)  3.8 rad/ $s ^ { 2 }$ 
B)  4.6 rad/ $s ^ { 2 }$ 
C)  5.3 rad/ $s ^ { 2 }$ 
D)  6.1 rad/ $s ^ { 2 }$ 
E)  6.8 rad/ $s ^ { 2 }$ 
A)  3.8 rad/ $s ^ { 2 }$ 
B)  4.6 rad/ $s ^ { 2 }$ 
C)  5.3 rad/ $s ^ { 2 }$ 
D)  6.1 rad/ $s ^ { 2 }$ 
E)  6.8 rad/ $s ^ { 2 }$

Question 7

As shown in the figure, a given force is applied to a rod in several different ways. In which case is the torque about the pivot P due to this force the greatest? 
1. 
2. 
3. 
4. 
5.

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
E)  5 
A)  1 
B)  2 
C)  3 
D)  4 
E)  5

Question 8

When Mary is 3.00 m from the center of a merry-go-round, her tangential speed is a constant 1.88 m/s.
(a) What is her angular speed in rad/s?
(b) What is the magnitude of her linear acceleration?

Accepted Answer

(a) 0.627

Question 9

A bicycle wheel has an initial angular speed of 7.2 rad/s. After turning through one-half  of a revolution, the angular speed is reduced to 2.2 rad/s. If the angular acceleration of the wheel was constant during the motion, how long will it take the wheel to make the one-half  revolution?

Accepted Answer

The answer of A bicycle wheel has an initial angular...

Question 10

In a laboratory experiment, a student brings up the rotational speed of a flywheel to 30.0 rpm. She then allows it to slow down on its own, and counts 240 revolutions before the apparatus uniformly comes to a stop. The moment of inertia of the flywheel is 0.0850 kg ∙ m2. What is the magnitude of the retarding torque on the flywheel?

Accepted Answer

A)  0.0425 N ∙ m 
B)  0.159 N ∙ m 
C)  0.0787 N ∙ m 
D)  0.000278 N ∙ m 
E)  0.0000136 N ∙ m 
A)  0.0425 N ∙ m 
B)  0.159 N ∙ m 
C)  0.0787 N ∙ m 
D)  0.000278 N ∙ m 
E)  0.0000136 N ∙ m

Question 11

Express the angular speed of an old 33 1/3 rpm LP in rad/s.

Accepted Answer

The answer of Express the angular speed of an old...

Question 12

A potter's wheel has the shape of a solid uniform disk of mass   and radius 0.65 m. It spins about an axis perpendicular to the disk at its center. A small 2.1 kg lump of very dense clay is dropped onto the wheel at a distance 0.41 m from the axis. What is the moment of inertia of the system about the axis of spin?

Accepted Answer

A)  1.8 kg ∙ m2 
B)  1.5 kg ∙ m2 
C)  0.40 kg ∙ m2 
D)  2.5 kg ∙ m2 
A)  1.8 kg ∙ m2 
B)  1.5 kg ∙ m2 
C)  0.40 kg ∙ m2 
D)  2.5 kg ∙ m2

Question 13

In the figure, point P is on the rim of a wheel of radius 2.0 m. At time t = 0, the wheel is at rest, and P is on the x-axis. The wheel undergoes a uniform counterclockwise angular acceleration of 0.010 rad/s2 about the center O.
(a) At time t = 0, what is the tangential acceleration of P?
(b) What is the linear speed of P when it reaches the y-axis?
(c) What is the magnitude of the net linear acceleration of P when it reaches the y-axis?
(d) How long after starting does it take for P to return to its original position on the x-axis?

Accepted Answer

(a) 0.020

Question 14

Two children, Ahmed and Jacques, ride on a merry-go-round. Ahmed is at a greater distance from the axis of rotation than Jacques. Which of the following are true statements? (There could be more than one correct choice.)

Accepted Answer

A)  Jacques has a greater angular speed than Ahmed. 
B)  Jacques and Ahmed have the same angular speed. 
C)  Jacques has a smaller angular speed than Ahmed. 
D)  Ahmed has a greater tangential speed than Jacques. 
E)  Jacques and Ahmed have the same tangential speed. 
A)  Jacques has a greater angular speed than Ahmed. 
B)  Jacques and Ahmed have the same angular speed. 
C)  Jacques has a smaller angular speed than Ahmed. 
D)  Ahmed has a greater tangential speed than Jacques. 
E)  Jacques and Ahmed have the same tangential speed.

Question 15

A scooter has wheels with a diameter of 120 mm. What is the angular speed of the wheels when the scooter is moving forward at 6.00 m/s?

Accepted Answer

A)  47.7 rpm 
B)  955 rpm 
C)  72.0 rpm 
D)  50.0 rpm 
E)  100 rpm 
A)  47.7 rpm 
B)  955 rpm 
C)  72.0 rpm 
D)  50.0 rpm 
E)  100 rpm

Question 16

At a certain instant, a compact disc is rotating at 210 rpm. What is its angular speed in rad/s?

Accepted Answer

A)  11 rad/s 
B)  22 rad/s 
C)  45 rad/s 
D)  69 rad/s 
E)  660 rad/s 
A)  11 rad/s 
B)  22 rad/s 
C)  45 rad/s 
D)  69 rad/s 
E)  660 rad/s

Question 17

The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P?

Accepted Answer

A)  A 
B)  B 
C)  C 
D)  D 
E)  The moment of inertia is the same for all of these objects. 
A)  A 
B)  B 
C)  C 
D)  D 
E)  The moment of inertia is the same for all of these objects.

Question 18

A machinist turns on the power on to a grinding wheel at time t = 0 s. The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of $96 \mathrm { rad } / \mathrm { s }$ The wheel is run at that angular velocity for 40 s and then power is shut off. The wheel slows down uniformly at $1.5 \mathrm { rad } / \mathrm { s } ^ { 2 }$ until the wheel stops. For how long a time after the power is shut off does it take the wheel to stop?

Accepted Answer

A)  64 s 
B)  62 s 
C)  66 s 
D)  68 s 
E)  70 s 
A)  64 s 
B)  62 s 
C)  66 s 
D)  68 s 
E)  70 s

Question 19

A 30-kg child stands at one end of a floating 20-kg canoe that is 5.0-m long and initially at rest in the water. The child then slowly walks to the other end of the canoe. How far does the canoe move in the water, assuming water friction is negligible?

Accepted Answer

A)  1.0 m 
B)  2.0 m 
C)  3.0 m 
D)  4.0 m 
E)  5.0 m 
A)  1.0 m 
B)  2.0 m 
C)  3.0 m 
D)  4.0 m 
E)  5.0 m

Question 20

There must be equal amounts of mass on both sides of the center of mass (or center of gravity) of a system.

Accepted Answer

A) True 
 B)False

Exam 7: Rotational Motion

A bicycle wheel has an outside diameter of 66 cm. Through what distance does a point on the rim move as the wheel rotates through an angle of 70°?

What is the angular speed, in rad/s, of a flywheel turning at 813.0 rpm?

A chicken is running in a circular path with an angular speed of 1.52 rad/s. How long does it take the chicken to complete one revolution?

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 horizontal?

As shown in the figure, a given force is applied to a rod in several different ways. In which case is the torque about the pivot P due to this force the greatest? 1. 2. 3. 4. 5.

When Mary is 3.00 m from the center of a merry-go-round, her tangential speed is a constant 1.88 m/s. (a) What is her angular speed in rad/s? (b) What is the magnitude of her linear acceleration?

A bicycle wheel has an initial angular speed of 7.2 rad/s. After turning through one-half of a revolution, the angular speed is reduced to 2.2 rad/s. If the angular acceleration of the wheel was constant during the motion, how long will it take the wheel to make the one-half revolution?

Express the angular speed of an old 33 1/3 rpm LP in rad/s.

Two children, Ahmed and Jacques, ride on a merry-go-round. Ahmed is at a greater distance from the axis of rotation than Jacques. Which of the following are true statements? (There could be more than one correct choice.)

A scooter has wheels with a diameter of 120 mm. What is the angular speed of the wheels when the scooter is moving forward at 6.00 m/s?

At a certain instant, a compact disc is rotating at 210 rpm. What is its angular speed in rad/s?

The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P?

A 30-kg child stands at one end of a floating 20-kg canoe that is 5.0-m long and initially at rest in the water. The child then slowly walks to the other end of the canoe. How far does the canoe move in the water, assuming water friction is negligible?

There must be equal amounts of mass on both sides of the center of mass (or center of gravity) of a system.

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