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Topic | Discussion | Learning Aids
| 7.1 THE IMPULSE–MOMENTUM THEOREM The impulse of a force is the product of the average force and the time interval during which the force acts: |
Impulse |

| (7.1)

| Impulse is a vector that points in the same direction as the average force. |
| The linear momentum of an object is the product of the object’s mass m and velocity : |
Linear momentum |

| (7.2)

| Linear momentum is a vector that points in the same direction as the velocity. The total linear momentum of a system of objects is the vector sum of the momenta of the individual objects. |
| The impulse–momentum theorem states that when a net force acts on an object, the impulse of the net force is equal to the change in momentum of the object: |
Impulse–momentum theorem |

| (7.4)

| 7.2 THE PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM External forces are those that agents external to the system exert on objects within the system. An isolated system is one for which the vector sum of the average external forces acting on the system is zero. |
| The principle of conservation of linear momentum states that the total linear momentum of an isolated system remains constant. For a two-body collision, the conservation of linear momentum can be written as |
Conservation of linear momentum |

| (7.7b)

| where m1 and m2 are the masses, and are the final velocities, and and are the initial velocities of the objects. |

Use Self-Assessment Test 7.1 to evaluate your understanding of Sections 7.1–7.2.

Elastic collision | 7.3 COLLISIONS IN ONE DIMENSION An elastic collision is one in which the total kinetic energy of the system after the collision is equal to the total kinetic energy of the system before the collision. |
Inelastic collision | An inelastic collision is one in which the total kinetic energy of the system is not the same before and after the collision. If the objects stick together after the collision, the collision is said to be completely inelastic. |
| 7.4 COLLISIONS IN TWO DIMENSIONS When the total linear momentum is conserved in a two-dimensional collision, the x and y components of the total linear momentum are conserved separately. For a collision between two objects, the conservation of total linear momentum can be written as |
Conservation of linear momentum |

| (7.9a)

| (7.9b)

| 7.5 CENTER OF MASS The location of the center of mass of two particles lying on the x axis is given by |
Location of center of mass |

| (7.10)

| where m1 and m2 are the masses of the particles and x1 and x2 are their positions relative to the coordinate origin. If the particles move with velocities v1 and v2, the velocity vcm of the center of mass is |
Velocity of center of mass |

| (7.11)

| If the total linear momentum of a system of particles remains constant during an interaction such as a collision, the velocity of the center of mass also remains constant. |

Use Self-Assessment Test 7.2 to evaluate your understanding of Sections 7.3–7.5.

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