### Linear Momentum Conservation

In this section, it is presented under which circumstances does the linear momentum of an object is conserved; i.e., it is unchanged. Starting from the relation between impulse and the change in linear momentum, , the condition for the conservation of linear momentum can be induced. The linear momentum is unchanged or conserved when . This occurs when the impulse is zero, that is, when the average force is zero, . The impulse can not be zero as a consequence of because this time interval corresponds to the time the force acts on the object and, if there is a force acting, this time interval can not be zero. On the other side, if there is not a force acting on the object (additionally, the time of action of a non existing force is meaningless), the impulse is already zero. In conclusion, the law of conservation of linear momentum can be stated as:

The linear momentum of an object is conserved, if no net force acts on the object.

Notices the close equivalence between the conservation of linear momentum and the Law of Inertia. In fact, the conservation of linear momentum is the mathematical expression of the law of inertia.

Conservation of Linear Momentum: If no net impulse acts on an object, the object conserves its linear momentum. Mathematically,

The three previous form are equivalent. However, they can be read in three different equivalent forms:

1. If no net impulse acts on an object, the change in linear momentum is zero.
2. If no net impulse acts on an object, the difference between the final linear momentum  and the initial linear momentum is zero.
3. If no net impulse acts on an object, the final linear momentum is the same as the initial linear momentum.

 Exercise

 1) Question a) b) N c) d) e) None of the above.

 The previous question correspond also to the problem of calculating the velocity of recoil of a gun. In this case, the bullet is much faster than the gun because the mass of the bullet is about 2.5% the mass of the gun (1 grain = 64.9 milligram and a bullet can be about 200 grains). Thus, the velocity of recoil of the gun is also about 2.5% of the velocity of the bullet.

 by Luis F. Sáez, Ph. D. Comments and Suggestions: LSaez@dallaswinwin.com