Question 1

Can two different forces, acting through the same point, produce the same torque on an object?

Accepted Answer

Yes,as long as the component of the force perpendicular to the line joining the axis to the force is the same for both forces.

Question 2

FIGURE 11-2  
-A figure skater is spinning slowly with arms outstretched. She brings her arms in close to her body and her angular speed increases dramatically. The speed increase is a demonstration of

Accepted Answer

A)  conservation of energy: her moment of inertia is decreased, and so her angular speed must increase to conserve energy. 
B)  conservation of angular momentum: her moment of inertia is decreased, and so her angular speed must increase to conserve angular momentum. 
C)  Newton's second law for rotational motion: she exerts a torque and so her angular speed increases. 
D)  This has nothing to do with mechanics, it is simply a result of her natural ability to perform. 
A)  conservation of energy: her moment of inertia is decreased, and so her angular speed must increase to conserve energy. 
B)  conservation of angular momentum: her moment of inertia is decreased, and so her angular speed must increase to conserve angular momentum. 
C)  Newton's second law for rotational motion: she exerts a torque and so her angular speed increases. 
D)  This has nothing to do with mechanics, it is simply a result of her natural ability to perform. B

Question 3

You are holding on to the axle of a spinning bicycle wheel with one hand on either side of the wheel. The top part of the wheel is moving away from you and the bottom is moving toward you and the axle is horizontal. In what direction do you need to apply a torque for the wheel to turn to the left?

Accepted Answer

A)  toward you 
B)  away from you 
C)  vertically up 
D)  vertically down 
E)  to your right 
A)  toward you 
B)  away from you 
C)  vertically up 
D)  vertically down 
E)  to your right A

Question 4

A horizontal, 2.00 m long, 3.00 kg uniform beam that lies along the east-west direction is acted on by two forces. At the east end of the beam, a 200 N force pushes downward. At the west end of the beam, a 200 N force pushed upward. What is the torque about the center of mass of the beam?

Accepted Answer

A)  800 N∙m north 
B)  zero 
C)  400 N∙m north 
D)  800 N∙m south 
E)  400 N∙m south 
A)  800 N∙m north 
B)  zero 
C)  400 N∙m north 
D)  800 N∙m south 
E)  400 N∙m south

Question 5

A mass of 375 g hangs from a string that is wrapped around the circumference of a pulley with a moment of inertia of 0.0125 kg∙m2 and a radius of 26.0 cm. When the mass is released, the mass accelerates downward and the pulley rotates about its axis as the string unwinds. What is the acceleration of the mass?

Accepted Answer

A)  19.9 m/s2 
B)  15.8 m/s2 
C)  13.1 m/s2 
D)  6.57 m/s2 
E)  3.28 m/s2 
A)  19.9 m/s2 
B)  15.8 m/s2 
C)  13.1 m/s2 
D)  6.57 m/s2 
E)  3.28 m/s2

Question 6

State the conditions for static equilibrium.

Accepted Answer

(1)The net force acting on the

Question 7

A solid wood door, 90.0 cm wide by 2.00 m tall has a mass of 35.0 kg. It is ajar and at rest. A ball with a mass of 500 g is thrown perpendicular to the door with a speed of 20.0 m/s and hits the door 60.0 cm from the hinged side. The ball rebounds with a speed of 16.0 m/s along the same line. What is the angular speed of the door after the collision?

Accepted Answer

A)  0.127 rad/s 
B)  0.925 rad/s 
C)  1.14 rad/s 
D)  2.28 rad/s 
E)  4.57 rad/s 
A)  0.127 rad/s 
B)  0.925 rad/s 
C)  1.14 rad/s 
D)  2.28 rad/s 
E)  4.57 rad/s

Question 8

A 120-kg refrigerator, 2.00 m tall and 85.0 cm wide has its center of mass at its geometrical center. You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator. The coefficient of static friction between the floor and the refrigerator is 0.300. Depending on where you push, the refrigerator may start to tip over before it starts to slide along the floor. What is the highest distance above the floor that you can push the refrigerator so that it won't tip before it begins to slide?

Accepted Answer

A)  0.710 m 
B)  1.00 m 
C)  1.21 m 
D)  1.42 m 
E)  1.63 m 
A)  0.710 m 
B)  1.00 m 
C)  1.21 m 
D)  1.42 m 
E)  1.63 m

Question 9

A ball with diameter 10. cm rolls without slipping on a horizontal table top. The moment of inertia of the ball is 2.2 × 10-3 kg- m2 and its translational speed is 0.45 m/s.
(a) What is its angular speed about its center of mass?
(b) What is its rotational kinetic energy?
(c) What is its angular momentum?

Accepted Answer

(a)9.0 rad

Question 10

A mass of 385 g hangs from one end of a string that goes over a pulley with a moment of inertia of 0.0125 kg∙m2 and a radius of 15.0 cm. A mass of 710 g hangs from the other end. When the masses are released, the larger mass accelerates downward, the lighter mass accelerates upward, and the pulley turns without the string slipping on the pulley. What is the tension in the string on the side of the 710-g mass?

Accepted Answer

A)  9.77 N 
B)  6.87 N 
C)  5.59 N 
D)  4.41 N 
E)  3.68 N 
A)  9.77 N 
B)  6.87 N 
C)  5.59 N 
D)  4.41 N 
E)  3.68 N

Question 11

An apparatus for measuring the mechanical equivalent of heat uses a crank to turn a small aluminum cylinder, which is being retarded by a belt. Friction with the belt heats up the cylinder, and the work done is then set equal to the heat gained by the cylinder. In one such experiment, the radius of the cylinder is 3.00 cm, the tension on one side of the belt is 50.0 N and on the other it is zero N. How much work is done turning the crank 212 times?

Accepted Answer

A)  2000 J 
B)  4000 J 
C)  19600 J 
D)  637 J 
E)  9800 J 
A)  2000 J 
B)  4000 J 
C)  19600 J 
D)  637 J 
E)  9800 J

Question 12

Two equal forces are applied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30° to the plane of the door. Which force exerts the greater torque?

Accepted Answer

A)  the first applied perpendicular to the door 
B)  the second applied at an angle 
C)  both exert equal non-zero torques 
D)  both exert zero torques 
E)  Additional information is needed. 
A)  the first applied perpendicular to the door 
B)  the second applied at an angle 
C)  both exert equal non-zero torques 
D)  both exert zero torques 
E)  Additional information is needed.

Question 13

Some students are discussing why a simple Atwood machine accelerates. Jane says that because of the unequal masses, gravity exerts a constant external torque on the two-mass and pulley system and thus its total angular momentum increases at a constant rate. Is Jane's explanation a valid one?

Accepted Answer

The answer of Some students are discussing why a simple...

Question 14

FIGURE 11-1  
-The rotating systems shown in Figure 11-1 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 15

A child is riding near the outer rim of a freely-rotating playground merry-go-round. What happens if the child walks towards the center?

Accepted Answer

The merry-go-round rotates mor

Question 16

The torque required to turn the crank on an ice cream maker is 4.50 Nm. How much work does it take to turn the crank through 300 full turns?

Accepted Answer

A)  4240 J 
B)  8480 J 
C)  2120 J 
D)  1350 J 
E)  2700 J 
A)  4240 J 
B)  8480 J 
C)  2120 J 
D)  1350 J 
E)  2700 J

Question 17

FIGURE 11-2  
-A puck moves on a horizontal air table. It is attached to a string that passes through a hole in the center of the table. As the puck rotates about the hole, the string is pulled downward very slowly and shortens the radius of rotation, so the puck gradually spirals in towards the center. By what factor will the puck's angular speed have changed when the string's length has decreased by 1/2?

Accepted Answer

A)  2 
B)  4 
C)    
D)  1 
E)  1/2 
A)  2 
B)  4 
C)    
D)  1 
E)  1/2

Question 18

Consider a bicycle wheel to be a ring of radius 30. cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20. N is applied tangentially to a sprocket of radius 4.0 cm for 4.0 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

Accepted Answer

The answer of Consider a bicycle wheel to be a...

Question 19

To determine the location of the center of mass of a car, the car is driven over a scale. When the front wheels are over the scale, the weight recorded by the scale is 5800 N, and when the rear wheels are over the scale, the scale reads 6500 N. The distance between the front and rear wheels is 3.20 m. How far behind the front wheels is the center of mass located?

Accepted Answer

A)  0.845 m 
B)  1.50 m 
C)  1.59 m 
D)  1.69 m 
E)  1.72 m 
A)  0.845 m 
B)  1.50 m 
C)  1.59 m 
D)  1.69 m 
E)  1.72 m

Question 20

FIGURE 11-4  
-The mobile shown in Figure 11-4 is perfectly balanced. What must be the masses of m1, m2, and m3?

Accepted Answer

m₁ = 1 g,m₂

Exam 11: Rotational Dynamics and Static Equilibrium

Can two different forces, acting through the same point, produce the same torque on an object?

FIGURE 11-2 -A figure skater is spinning slowly with arms outstretched. She brings her arms in close to her body and her angular speed increases dramatically. The speed increase is a demonstration of

You are holding on to the axle of a spinning bicycle wheel with one hand on either side of the wheel. The top part of the wheel is moving away from you and the bottom is moving toward you and the axle is horizontal. In what direction do you need to apply a torque for the wheel to turn to the left?

A horizontal, 2.00 m long, 3.00 kg uniform beam that lies along the east-west direction is acted on by two forces. At the east end of the beam, a 200 N force pushes downward. At the west end of the beam, a 200 N force pushed upward. What is the torque about the center of mass of the beam?

State the conditions for static equilibrium.

Two equal forces are applied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30° to the plane of the door. Which force exerts the greater torque?

Some students are discussing why a simple Atwood machine accelerates. Jane says that because of the unequal masses, gravity exerts a constant external torque on the two-mass and pulley system and thus its total angular momentum increases at a constant rate. Is Jane's explanation a valid one?

FIGURE 11-1 -The rotating systems shown in Figure 11-1 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,

A child is riding near the outer rim of a freely-rotating playground merry-go-round. What happens if the child walks towards the center?

The torque required to turn the crank on an ice cream maker is 4.50 Nm. How much work does it take to turn the crank through 300 full turns?

Consider a bicycle wheel to be a ring of radius 30. cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20. N is applied tangentially to a sprocket of radius 4.0 cm for 4.0 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

FIGURE 11-4 -The mobile shown in Figure 11-4 is perfectly balanced. What must be the masses of m1, m2, and m3?

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FIGURE 11-4 -The mobile shown in Figure 11-4 is perfectly balanced. What must be the masses of m₁, m₂, and m₃?