# Linear Momentum and Impulse

**Linear momentum of a force:**

Linear momentum simply is the product of its mass and linear velocity. The body having more mass have more momentum than that of smaller one keeping velocity constant. It is denoted by P. Mathematically,

P =m×v

The unit of linear momentum is kgms^{-1 }. It is a vector quantity. A moving body always posses momentum. Momentum is always conserved in all types of collision.

**Impulse of a force:**

When a very strong force acts for a very short period of time, it is said to be impulse. If someone made you push from the backside with an enormous speed, you become afraid and oscillate. It is an example of impulse. It is denoted by I. Mathematically,

$$\text{I} = \text{F}_{av} × \delta \text{T}$$

**Relation between impulse and momentum:**

We know force is equal to the rate of change in momentum.

$$F = \frac{dP}{dT}$$

$$or, \text{F.dT = dP}$$

Integrating both sides,

$$ \int_{0}^{t} FdT = \int_{P_1}^{P_2} dP$$

$$or, T= [P]^{P_2}_{P_1}$$

$$or, T = P_2 – P1$$

Hence, we can say that, impulse is the rate of change in momentum.

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