# Mass and Momentum

## What is Mass?

We can define mass as the inherent property of matter. It is the measure of the inertia of a body, mass tells us how much matter there is in a body, we can measure the mass of a body on earth by measuring the force of gravity acting on it, the SI unit of mass is kilogram (kg).

Remember mass is not the same as weight, even though we measure the mass of a body by measuring its weight, a body with the same mass weighs differently on the moon than it weighs here on earth, mass is one property of matter that doesn’t change easily.

A bowling ball has more mass than football because it has more matter in it, hence, it weighs more too, and most of the physical quantities of matter are derived from mass, and mass plays a very important role in physics. Momentum, inertia and other properties of matter are all because of mass.

Mass is a form of energy; it is energy at rest. In 1905 Albert Einstein formulated the theory of special relativity;

E = $mc^2$

which states that energy is mass times the speed of light, as speed of light is approximately $3\times 10^{8}m/s$, the energy inside 1 kilogram of matter would be a whopping 90000000000 joules of energy, that’s a lot of energy inside just 1 kilogram of matter, this energy can be tapped by recent advancements in nuclear technology and by means of nuclear fission, and a small amount of matter is converted into clean energy.

Acceleration of a body is $\propto \frac{1}{Mass}$

Therefore for a given force: a $\propto \frac{1}{Mass}$

## What is Momentum?

We can define momentum as the quantity of motion of the body. It is measured by $mass\times velocity$, as momentum depends upon velocity, and it depends on the direction of the motion of the body as well.

Momentum = Mass X Velocity

p = mv

The S.I. unit of momentum is kilogram metre per second($kgms^{-1}$)

Imagine two friends’ Sam and Max running in the playground; Sam weighs 30 kilograms and Max weighs 40 kilograms, both of them are running at the same speed in the same direction.

• (a) Who has more momentum, and why?
• (b) Who will get hurt more if they hit a wall?

The answer to both the above questions would be Max, because he has more momentum, as the velocity of Sam and Max is same, their momentum will depend upon their mass, therefore max will have more momentum than Sam.

The law of conservation of momentum states that the total momentum of a closed system does not change, which means that if two bodies collide with each other, their total momentum after the collision will be equal to their momentum before the collision.

Let’s get some terms clear:

### What is Weight?

Weight is the force experienced by the body due to gravity, SI unit of weight is Newton (N) because the weight is essentially a force. Weight can vary from place to place depending on gravity.

### What is Density?

Density is the amount of matter in unit volume or mass per unit volume, the Greek letter ρ (rho) is used to denote density, and the SI unit of density is kg/m3.

### What is Inertia?

Inertia is the resistance offered by matter to acceleration, technically mass is the measure of inertia.

Stay tuned with BYJU’S to learn more about mass and momentum, conservation of linear momentum and much more.

#### Practise This Question

A large tank filled with water to a height 'h' is to be emptied through a small hole at the bottom. The ratio of time taken for the level of water to fall from h to h/2 and from h/2 to zero is