Momentum

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What is Momentum?

Imagine that you are running on a straight road. If someone asks you to stop, what will happen? Will you be able to stop yourself immediately? No! You will be able to stop yourself only after a second or two. It happens because your body has momentum which tends to take you further with it.

Now, what would have happened if you were running at a greater speed? Yes, you would have taken more time to stop. Also, if you were heavier, even then it would have taken you more time to come to a standstill for the same velocity.

This means, the more the mass and the velocity, the greater is the momentum. Thus, Momentum is directly proportional to mass and velocity.

Mathematically it is expressed as the product of mass and velocity. It is denoted by the

letter ‘p’. So, we can write the formula of momentum as,

p = m X v

 And the SI unit of momentum is kg ms-1.

Now, when a net force is applied, the velocity of the object changes and when velocity changes, its momentum also changes.

So, net force is nothing but the rate of change of momentum. Therefore,

Net force = (p2  – p1)/t

 where, p1 = initial momentum, p2 = final momentum and t = time taken

The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force.

Understanding Newton’s second law using momentum

If v is the final velocity and u is the initial velocity,

Net force = (mv – mu) / t   (Since p = m x v) if we denote Net force by F, then

F  = m(v – u) / t

v-u is the change in velocity

This means (v-u)/t is the rate of change of velocity; and rate of change of velocity is called acceleration

(v-u)/t = a

Substituting this value in the above equation, we get,

F = m X a

which is nothing but Newton’s second law of motion.

Understanding Newton’s first law using momentum

Let us look at an equation we discussed earlier:

F  = m(v – u) / t

This can be written as:

Ft = mv – mu

If the net force is zero, i.e. F = 0

(0) t = mv – mu 0 = mv – mu

mv = mu v = u

So, v = u tells us that the object is either at rest, when v = u = 0, or moving at constant velocity,

when v = u ≠ 0. And this nothing but Newton’s first law.