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Chapter

9

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Image BankChapter

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Baseball Player

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A Bocce Ball and a Hollow Plastic Ball

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Force on a Baseball

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Car Crash

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Average Force (1)

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Average Force (2)

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Diver Getting Ready to Dive

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Diver Changing Her Moment of Inertia

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Ice-Skater

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Two-Particle Collisions

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Speed

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Bullet Striking a Bag of Flour

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Two In-line Skaters (1)

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Ion Engine

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An Astronaut Firing a Thruster Pistol

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Billiard Balls Colliding

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Two Cars Colliding

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A Spinning Ice-Skater (1)

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A Spinning Ice-Skater (2)

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A Top

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Car Crash

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Gyroscope

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A Cart Rolling Down the Incline

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Cart System

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Cosmos 1

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Chapter Assessment (Q. 49)

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Standardized Test Practice (Q. 6)

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TransparenciesChapter

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Impulse

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9 Video Clips and Animations

Conservation of Momentum

Chapter


Using the Impulse-Momentum Theorem

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Angular Momentum (1)

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Angular Momentum (2)

Chapter


Recoil

Chapter


Two-Dimensional Collisions

Chapter


Chapter Summary

When doing a momentum problem, first examine the system before and after the event.

The momentum of an object is the product of its mass and velocity and is a vector quantity.

Impulse and Momentum

Section

9.1

The impulse on an object is the average net force exerted on the object multiplied by the time interval over which the force acts.

Chapter Summary

The impulse on an object is equal to the change in momentum of the object.

Impulse and Momentum

Section

9.1

The angular momentum of a rotating object is the product of its moment of inertia and its angular velocity.

The angular momentum of a rotating object is the product of its moment of inertia and its angular velocity.

Chapter Summary

According to Newton’s third law of motion and the law of conservation of momentum, the forces exerted by colliding objects on each other are equal in magnitude and opposite in direction.

Momentum is conserved in a closed, isolated system.


Section

9.2

The law of conservation of momentum can be used to explain the propulsion of rockets.

Chapter Summary

Vector analysis is used to solve momentum-conservation problems in two dimensions.

The law of conservation of angular momentum states that if there are no external torques acting on a system, then the angular momentum is conserved.


Section

9.2

Because angular momentum is conserved, the direction of rotation of a spinning object can be changed only by applying a torque.


A 1500-kg car hits a wall with a velocity of 20 m/s and immediately comes to rest. What is the final momentum of the car?

Question 1

Chapter

9

A. (1500 kg)(20 m/s)

B. (1500 kg)(–20 m/s)

C. 0 kg·m/s

D. (1500 kg)(20 m/s)2


Answer: C

Answer 1

Chapter

9

Reason: Momentum of an object is equal to the mass of the object times the object’s velocity.

Pf = mvf

Since the car comes to rest, vf = 0.

Therefore, Pf = (1500 kg)(0 m/s) = 0 kg·m/s.


If no net force is acting on an object, its velocity remains the same. Explain why the angular velocity can change when no torque is acting on an object.

Question 2

Chapter

9


If there is no torque acting on an object, its angular momentum is constant. In case of angular momentum, the object’s angular velocity may not remain the same. This is because the moment of inertia depends on the object’s mass and the way it is distributed about the axis of rotation or revolution. Thus, the angular velocity of an object can change even if no torque is acting on it.

Answer 2

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9


Why does a planet move faster when it is nearer to the sun? Explain on the basis of the change in angular velocity of the planet.

Question 3

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9


When a planet is orbiting the sun, the torque on the planet is zero because gravitational force acts toward the center of the orbit. Therefore, the planet’s angular momentum remains constant throughout its orbital motion. When the distance between the planet and the sun decreases, the planet’s moment of inertia of revolution in the orbit about the sun also decreases. Thus, the planet’s angular velocity increases and it moves faster.

Answer 3

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Can the momentum of a bicycle and a car be the same?

Question 4

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Yes, because momentum of an object is equal to the mass of the object times the object’s velocity. Hence, if a bicycle with very little mass as compared to a car runs with a greater velocity, and on the other hand, if the car runs with a smaller velocity. It may happen that the product of mass and velocity of the bicycle become equal to the product of mass and velocity of the car. That is, there is a possibility that a car and a bicycle may have the same momentum.

Answer 4

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How can an ice-skater increase his angular velocity without external torque?

Question 5

Chapter

9

A. By decreasing his moment of inertia.

B. By increasing the angular momentum.

C. By increasing the linear velocity.

D. By increasing his moment of inertia.


Answer: A

Answer 5

Chapter

9

Reason: Without an external torque, the angular momentum does not change. Thus, the ice-skater’s increased angular velocity must be accompanied by a decreased moment of inertia. By pulling his arms close to his body, the ice-skater brings more mass closer to the axis of rotation, thereby decreasing the radius of rotation and decreasing his moment of inertia.


1. When a star that is much larger than the Sun nears the end of its lifetime, it begins to collapse, but continues to rotate. Which of the following describes the conditions of the collapsing star’s moment of inertia (I), angular momentum (L), and angular velocity (ω)?

Multiple Choice

Chapter

9

A. I increases, L stays constant, ω decreases

B. I decreases, L stays constant, ω increases

C. I increases, L stays increases, ω increases

D. I increases, L stays increases, ω constant


2. A 40.0-kg ice-skater glides with a speed of 2.0 m/s toward a 10.0-kg sled at rest on the ice. The ice-skater reaches the sled and holds on to it. The ice-skater and the sled then continue sliding in the same direction in which the ice-skater was originally skating. What is the speed of the ice-skater and the sled after they collide?

Multiple Choice

Chapter

9

A. 0.4 m/s

B. 0.8 m/s

C. 1.6 m/s

D. 3.2 m/s


3. A bicyclist applies the brakes and slows the motion of the wheels. The angular momentum of each wheel then decreases from 7.0 kg·m2/s to 3.5 kg·m2/s over a period of 5.0 s. What is the angular impulse on each wheel?

Multiple Choice

Chapter

9

A. 0.7 kg·m2/s

B. 1.4 kg·m2/s

C. 2.1 kg·m2/s

D. 3.5 kg·m2/s


4. A 45.0-kg ice-skater stands at rest on the ice. A friend tosses the skater a 5.0-kg ball. The skater and the ball then move backward across the ice with a speed of 0.50 m/s. What was the speed of the ball at the moment just before the skater caught it?

Multiple Choice

Chapter

9

A. 2.5 m/s

B. 3.0 m/s

C. 4.0 m/s

D. 5.0 m/s


5. What is the difference in momentum between a 50.0-kg runner moving at a speed of 3.00 m/s and a 3.00x103-kg truck moving at a speed of only 1.00 m/s?

Multiple Choice

Chapter

9

A. 1275 kg.m/s

B. 2550 kg.m/s

C. 2850 kg.m/s

D. 2950 kg.m/s

6. When the large gear in the diagram rotates, it turns the small gear in the opposite direction at the same angular speed. The larger gear has twice the radius and four times the mass of the smaller gear. What is the angular momentum of the larger gear as a function of the angular momentum of the smaller gear? Hint: The moment of inertia for a disk is , where m is the mass and r is the radius of the disk.

Multiple Choice

Chapter

9 Standardized Test Practice

A. 1275 kg·m/s

B. 2550 kg·m/s

C. 2850 kg·m/s

D. 2950 kg·m/s


7. A force of 16 N exerted against a rock with an impulse of 0.8 kg.m/s causes the rock to fly off the ground with a speed of 4.0 m/s. What is the mass of the rock?

Multiple Choice

Chapter

9

A. 0.2 kg

B. 0.8 kg

C. 1.6 kg

D. 4.0 kg


8. A 12.0-kg rock falls to the ground. What is the impulse on the rock if its velocity at the moment it strikes the ground is 20.0 m/s?

Extended Answer

Chapter

9

End of Chapter Resource File

Momentum and Its ConservationChapter

9

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