Physics Topics can be both theoretical and experimental, with scientists using a range of tools and techniques to understand the phenomena they investigate.

## Introduction to Momentum with Examples

In order to understand Newton’s second law of motion, we should first know the meaning of the term ‘momentum’ of a moving body (or moving object). This is discussed below.

We know that a cricket ball is much more heavy than a tennis ball. Suppose we throw a cricket ball and a tennis ball, both with the same speed or velocity. It will be found that more force is required to stop the cricket ball (which has more mass) and less force is required to stop the tennis ball (which has less mass).

We conclude that the force required to stop a moving body is directly proportional to its mass. Now, if we throw two cricket balls of the same mass at different speeds or velocities, it will be found that more force is required to stop that cricket ball which is moving with higher velocity and less force is required to stop the cricket ball moving with lower velocity. So, we conclude that the force required to stop a moving body is also directly proportional to its velocity. Thus, the quantity of motion in a body depends on the mass and velocity of the body. This gives us another term known as “momentum”. The momentum of a body is defined as the product of its mass and velocity.

Thus, Momentum = mass × velocity

or, p = m × v

where p = momentum

m = mass of the body

and v = velocity (or speed) of the body

It is clear that if a body is at rest, its velocity is zero and hence its momentum is also zero. Thus, the total momentum of the gun and bullet before firing is zero because their velocity is zero. Momentum is a vector quantity and takes place in the direction of velocity. We have just seen that, momentum = mass × velocity. Now, mass is measured in kilograms (kg) and velocity is measured in metres per second (m/s), so the SI unit of momentum is kilogram metres per second which is written as kg.m/s or kg.m s^{-1}.

Every moving body possesses momentum. Since momentum depends on the mass and velocity of a body, so a body will have a large momentum :

(a) if its mass is large, or

(b) if its velocity (speed) is large, or

(c) if both its mass and velocity (speed) are large. We will now discuss some everyday situations which involve large momentum. A karate player can break a pile of tiles or a slab of ice with a single blow of his hand. This is because a karate player strikes the pile of tiles or the slab of ice with his hand very, very

fast. In doing so, the large momentum of the fast moving hand is reduced to zero in a very, very short time. This exerts a very large force on the pile of tiles or the ice slab which is sufficient to break them apart.

Though a cricket ball is not very heavy but when it is thrown with a high speed (or high velocity), it acquires a very large momentum and sometimes hurts the batsman. This is why a batsman often ducks to a bouncer. On the other hand, a car or bus may not be running at a high speed (or high velocity) but because of its high mass, it has a very high momentum which may hurt the person coming in its way. It is a common observation that road accidents at high speeds are very much worse than accidents at low speeds.

This is because the momentum of vehicles running at high speeds is very high and causes a lot of damage to the vehicles and injuries to passengers during the collision. Thus, we are afraid of a moving cricket ball or a running vehicle because of the combined effect of their mass and velocity which is called momentum. From this discussion we conclude that the combined effect of mass and velocity of a body is taken into account by a physical quantity called momentum. In fact, momentum is considered to be a measure of the quantity of motion of a moving body. We can feel what momentum is if we happen to collide with a person running at top speed ! We will now solve a problem based on momentum.

Example Problem.

What is the momentum of a man of mass 75 kg when he walks with a uniform velocity of 2 m/s ?

Solution.

We know that:

Momentum = mass × velocity

= m × v

Here, Mass, m= 75 kg

And, Velocity, v = 2 m/s

Putting these values in the above formula, we get:

Momentum = 75 × 2 kg.m/s

= 150 kg.m/s