More properly known as linear momentum, momentum is simply the product of mass and velocity. Due to the fact that it is derived from a vector, namely velocity, momentum is also a vector. In this writeup, boldface will be used to express vectors, and italics to represent the magnitude of a vector or scalars. Momentum is usually represented by the letter p:

p = mv

Since velocity depends on reference frames, all magnitudes must include the reference frame. Looking at the equation, we see that a larger massed object will have a greater momentum than a smaller massed one with the same velocity. What this basically means is that a big truck going at 70 km/h can smash your house, but a 2 year old baby going at 1 m/s will not (at least by walking into it).

Since velocity can only be changed by applying a force, it follows that momentum also must be changed in the same manner. As a matter of fact, Newton's second law was originally stated in a more general form, dealing with momentum (which he referred to as quantity of motion). The original second law, paraphrased, is:

The rate of change of momentum of a body is proportional to the net force applied to it.


ΣF = Δpt

Where ΣF stands for its normal value, the net force applied to an object and Δt is the change in time. Some simple arithmetic (which is left to the reader) is all that is required to translate the above equality to the familiar ΣF = ma.

Conservation of Momentum

A simple concept -- the total momentum of an isolated system is the same at all times (i.e., no momentum is gained or lost).

The total momentum of an isolated system of bodies remains constant.

But 'Wait!', you say. 'What if we drop a ball from 5 metres? It will accelerate, thus increasing its momentum, and then reach a velocity of zero, reducing its momentum to zero. This means there was a loss of momentum.' Not so. The solution in all such cases is to expand the system. In this case, we would include the Earth. In the case of the ball, all of the ball's momentum was transferred to the Earth. However, since the mass of the Earth is so large, very little change in velocity is needed to impart to the Earth the same momentum as the ball. This idea is extremely important in the field of Mechanics.