Question 1

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger angular speed?

Accepted Answer

A) Child A 
B) Child B 
C) They have the same zero angular speed. 
D) They have the same non-zero angular speed. 
E) There is not enough information given to answer the question. 
A) Child A 
B) Child B 
C) They have the same zero angular speed. 
D) They have the same non-zero angular speed. 
E) There is not enough information given to answer the question. D

Question 2

A child is riding on a merry-go-round, which is accelerating. What is the relationship between the angular speed ω and the angular acceleration α of the merry-go-round when the tangential and centripetal accelerations of the child are equal?

Accepted Answer

α = ω<sup>2</sup>

Question 3

When a rigid body rotates about a fixed axis all the points in the body have the same angular displacement.

Accepted Answer

A) True 
 B)False  True

Question 4

A wheel of radius R is rolling on a horizontal surface. Its center is moving forward with speed v. A point on the wheel a distance r/3 below the center is moving forward at a speed 2v/3. The wheel is

Accepted Answer

A) rolling without slipping. 
B) not rotating at all. 
C) made of rubber. 
D) slipping because its angular speed is too low to be rolling without slipping. 
E) slipping because its angular speed is too high to be rolling without slipping. 
A) rolling without slipping. 
B) not rotating at all. 
C) made of rubber. 
D) slipping because its angular speed is too low to be rolling without slipping. 
E) slipping because its angular speed is too high to be rolling without slipping.

Question 5

A spool whose inner core has a radius of 1.00 cm and whose end caps have a radius of 1.50 cm has a string tightly wound around the inner core. The spool is free to roll without slipping on a horizontal surface. If the string unwinds horizontally from the bottom of the core with a constant speed of 25.0 cm/s, what is the speed of the spool?

Accepted Answer

A) 5.00 cm/s 
B) 15.0 cm/s 
C) 25.0 cm/s 
D) 37.5 cm/s 
E) 75.0 cm/s 
A) 5.00 cm/s 
B) 15.0 cm/s 
C) 25.0 cm/s 
D) 37.5 cm/s 
E) 75.0 cm/s

Question 6

A person pushes on a doorknob with a force of 5.00 N perpendicular to the surface of the door. The doorknob is located 0.800 m from axis of the hinges of the door. The door begins to rotate with an angular acceleration of 2.00 rad/s2. What is the moment of inertia of the door about the hinges?

Accepted Answer

A) 2.00 kg∙m2  
B) 1.00 kg∙m2  
C) 12.5 kg∙m2  
D) 8.00 kg∙m2  
E) 6.40 kg∙m2  
A) 2.00 kg∙m2  
B) 1.00 kg∙m2  
C) 12.5 kg∙m2  
D) 8.00 kg∙m2  
E) 6.40 kg∙m2

Question 7

A man is holding an 8.00-kg vacuum cleaner at arm's length, a distance of 0.550 m from his shoulder. What is the torque on the shoulder joint if the arm is horizontal?

Accepted Answer

A) 0.242 Nm 
B) 4.40 Nm 
C) 43.2 Nm 
D) 14.5 Nm 
E) 0 Nm 
A) 0.242 Nm 
B) 4.40 Nm 
C) 43.2 Nm 
D) 14.5 Nm 
E) 0 Nm

Question 8

Rolling without slipping depends on static friction between the rolling object and the ground.

Accepted Answer

A) True 
 B)False

Question 9

As you are leaving a building, the door opens outward. If the hinges on the door are on your right, what is the direction of the angular velocity of the door as you open it?

Accepted Answer

A) up 
B) down 
C) to your left 
D) to your right 
E) forwards 
A) up 
B) down 
C) to your left 
D) to your right 
E) forwards

Question 10

Suppose a solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

Accepted Answer

A) the mass of the sphere. 
B) the radius of the sphere. 
C) both the mass and the radius of the sphere. 
D) neither the mass nor the radius of the sphere. 
A) the mass of the sphere. 
B) the radius of the sphere. 
C) both the mass and the radius of the sphere. 
D) neither the mass nor the radius of the sphere.

Question 11

FIGURE 10-1  
-The rotating systems shown in Fig. 10-1 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,

Accepted Answer

A) the block at left lands first. 
B) the block at right lands first. 
C) both blocks land at the same time. 
D) it is impossible to tell which block reaches the bottom first. 
A) the block at left lands first. 
B) the block at right lands first. 
C) both blocks land at the same time. 
D) it is impossible to tell which block reaches the bottom first.

Question 12

When a rigid body rotates about a fixed axis all the points in the body have the same linear displacement.

Accepted Answer

A) True 
 B)False

Question 13

Suppose a solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

Accepted Answer

A) the mass of the sphere. 
B) the radius of the sphere. 
C) both the mass and the radius of the sphere. 
D) neither the mass nor the radius of the sphere. 
A) the mass of the sphere. 
B) the radius of the sphere. 
C) both the mass and the radius of the sphere. 
D) neither the mass nor the radius of the sphere.

Question 14

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down a 35° incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is given by I= (2/5)MR2.
(a) Calculate the linear speed of the sphere when it reaches the bottom of the incline.
(b) Determine the angular speed of the sphere at the bottom of the incline.
(c) Does the linear speed depend on the radius or mass of the sphere? Does the angular speed depend on the radius or mass of the sphere?

Accepted Answer

(a) 7.5 m/s
(b) 50 rad/s
(c) T

Question 15

Consider a hoop of radius R and mass M rolling without slipping. Which form of kinetic energy is larger, translational or rotational?

Accepted Answer

A) Translational kinetic energy is larger. 
B) Rotational kinetic energy is larger. 
C) Both are equal. 
D) You need to know the speed of the hoop to tell. 
E) You need to know the acceleration of the hoop to tell. 
A) Translational kinetic energy is larger. 
B) Rotational kinetic energy is larger. 
C) Both are equal. 
D) You need to know the speed of the hoop to tell. 
E) You need to know the acceleration of the hoop to tell.

Question 16

FIGURE 10-3  
-Fig. 10-3 illustrates a simplified roller bearing. The outer hollow cylinder has a radius of 1.2 cm and is stationary. The inner cylinder has a radius of 1.0 cm and is rotating at 11 rpm. Between the two cylinders are several small cylinders with a radius of 0.10 cm, which roll without slipping on both the inner and outer cylinders. Only one of these cylinders is shown in the figure. What is the angular speed of the small cylinders?

Accepted Answer

A) 12 rpm 
B) 10 rpm 
C) 20 rpm 
D) 62 rpm 
E) 55 rpm 
A) 12 rpm 
B) 10 rpm 
C) 20 rpm 
D) 62 rpm 
E) 55 rpm

Question 17

FIGURE 10-1  
-The rotating systems shown in Fig. 10-1 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 =   tR. 
D) tL = 2 tR. 
E) tL = 4 tR. 
A) tL =   tR. 
B) tL = tR. 
C) tL =   tR. 
D) tL = 2 tR. 
E) tL = 4 tR.

Question 18

A solid disk is released from rest and rolls without slipping down an inclined plane that makes an angle of 25.0° with the horizontal. What is the speed of the disk after it has rolled 3.00 m, measured along the plane?

Accepted Answer

A) 2.04 m/s 
B) 3.53 m/s 
C) 4.07 m/s 
D) 5.71 m/s 
E) 6.29 m/s 
A) 2.04 m/s 
B) 3.53 m/s 
C) 4.07 m/s 
D) 5.71 m/s 
E) 6.29 m/s

Question 19

A string is wrapped around a pulley with a radius of 2.0 cm. The pulley is initially at rest. A constant force of 50 N is applied to the string, causing the pulley to rotate and the string to unwind. If the string unwinds 1.2 m in 4.9 s, what is the moment of inertia of the pulley?

Accepted Answer

A) 0.17 kg∙m2  
B) 17 kg∙m2  
C) 14 kg∙m2  
D) 0.20 kg∙m2  
E) 0.017 kg∙m2  
A) 0.17 kg∙m2  
B) 17 kg∙m2  
C) 14 kg∙m2  
D) 0.20 kg∙m2  
E) 0.017 kg∙m2

Question 20

The moment of inertia of a uniform rod (about its center) is given by I = M   /12. What is the kinetic energy of a 120-cm rod with a mass of 450 g rotating about its center at 3.60 rad/s?

Accepted Answer

A) 0.350 J 
B) 4.20 J 
C) 0.700 J 
D) 0.960 J 
E) 2.10 J 
A) 0.350 J 
B) 4.20 J 
C) 0.700 J 
D) 0.960 J 
E) 2.10 J

Exam 10: Rotational Motion

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger angular speed?

A child is riding on a merry-go-round, which is accelerating. What is the relationship between the angular speed ω and the angular acceleration α of the merry-go-round when the tangential and centripetal accelerations of the child are equal?

When a rigid body rotates about a fixed axis all the points in the body have the same angular displacement.

A wheel of radius R is rolling on a horizontal surface. Its center is moving forward with speed v. A point on the wheel a distance r/3 below the center is moving forward at a speed 2v/3. The wheel is

A person pushes on a doorknob with a force of 5.00 N perpendicular to the surface of the door. The doorknob is located 0.800 m from axis of the hinges of the door. The door begins to rotate with an angular acceleration of 2.00 rad/s2. What is the moment of inertia of the door about the hinges?

A man is holding an 8.00-kg vacuum cleaner at arm's length, a distance of 0.550 m from his shoulder. What is the torque on the shoulder joint if the arm is horizontal?

Rolling without slipping depends on static friction between the rolling object and the ground.

As you are leaving a building, the door opens outward. If the hinges on the door are on your right, what is the direction of the angular velocity of the door as you open it?

Suppose a solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

FIGURE 10-1 -The rotating systems shown in Fig. 10-1 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,

When a rigid body rotates about a fixed axis all the points in the body have the same linear displacement.

Suppose a solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

Consider a hoop of radius R and mass M rolling without slipping. Which form of kinetic energy is larger, translational or rotational?

A solid disk is released from rest and rolls without slipping down an inclined plane that makes an angle of 25.0° with the horizontal. What is the speed of the disk after it has rolled 3.00 m, measured along the plane?

A string is wrapped around a pulley with a radius of 2.0 cm. The pulley is initially at rest. A constant force of 50 N is applied to the string, causing the pulley to rotate and the string to unwind. If the string unwinds 1.2 m in 4.9 s, what is the moment of inertia of the pulley?

The moment of inertia of a uniform rod (about its center) is given by I = M /12. What is the kinetic energy of a 120-cm rod with a mass of 450 g rotating about its center at 3.60 rad/s?

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A person pushes on a doorknob with a force of 5.00 N perpendicular to the surface of the door. The doorknob is located 0.800 m from axis of the hinges of the door. The door begins to rotate with an angular acceleration of 2.00 rad/s². What is the moment of inertia of the door about the hinges?