1. Conservation of momentum

It follows from Newton's second and third laws that if no external forces act on a system of colliding bodies, then the total momentum of the bodies has the same magnitude and direction before and after the collisions.

This is called the principle of CONSERVATION OF MOMENTUM, and is useful in solving problems in dynamics (the physics and mathematics of moving objects).

Click to see an animation

For example, if two bodies of masses m1 and m2 having initial velocities vi1 and vi2 collide and then separate with velocities vf1 and vf2, as shown in the animation above, the equation for the conservation of momentum is

The above expression is a mathematical statement of the Law of Conservation of Linear Momentum (), which may be stated as

Law of Conservation of Linear Momentum
"In an isolated system (that is a system where no other forces are acting) the total momentum of the system is constant."

It is important to realise that the law only applies to ISOLATED SYSTEMS, that is, systems where the only forces that are acting are those between the inteacting bodies. In the sort of problems that you might encounter at Grades 11 and 12 levels, you may assume that you are dealing with isolated systems, unless told otherwise. An example of a system that is not isolated would be two railway trucks colliding. Here, apart from the forces between the colliding trucks, there is the force of friction between the wheels of the trucks and the rails. Normally, such frictional forces are ignored.

2. Additional questions

Newton's three laws of motion

First law: A body will continue in a state of rest or uniform motion in a straight line unless acted upon by a resultant force.

Second law: The rate of change of momentum of a body is proportional to the force applied to that body and in the direction of that force.


When a resultant force is applied to a body it produces an acceleration that is directly proportional to the resultant force and inversely proportional to the mass of the body).

Third law: For every force (or action) between two bodies there is always an equal but oppositely directed force (or reaction).