# Linear Momentum

## Linear Momentum

The linear momentum of a particle of mass m moving with a velocity v is defined to be the product of the mass and velocity. It is a vector quantity. It is mathematically.

$$Momentum\left( p \right)=Mass\left( m \right)\times Velocity\left( v \right)$$,

1) Linear momentum of a body is the quantity of motion contained in the body.

2) It is measured in terms of the force required to stop the body in unit time.

3) It is a vector quantity and its direction is the same as the direction of velocity of the body.

4) Units: kg.m/sec in S.I units; Dimensions: $$\left[ ML{{T}^{-1}} \right]$$

6) If two objects of different masses have same momentum, the lighter body possesses greater velocity.

$$p={{m}_{1}}{{v}_{1}}={{m}_{2}}{{v}_{2}}=Constant$$,

$$\therefore \,\,\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}}$$ $$\Rightarrow \,v\,\,\propto \,\,\frac{1}{m}$$     (As $$p$$ is constant)

7) For a given body, $$p\propto v$$

8) For different bodies moving with same velocities, $$p\propto m$$