Momentum and Newton’s Second Law of Motion Linear momentum : Momentum of body is the physical quantity of motion possessed by the body and mathematically. It is defined as the product of mass and velocity of the body.
As the linear momentum or simply momentum is equal to a scalar times a vector (velocity), it is therefore a vector quantity and is denoted by \(\vec{p}\).
The momentum of a body of mass m moving with velocity \(\vec{v}\) is given by the relation :
\(\vec{p}=m \vec{v}\)
Dimensional formula = [M1L1T-1]
Unit = Kg m/s
Suppose that a ball of mass m1 and a car of mass m2 (m2 > m1) are moving with the same velocity v. If P1 and p2 are momentum of ball and car respectively then :
\(\frac{p_{1}}{p_{2}}=\frac{m_{1} v}{m_{2} v}\) or \(\frac{p_{1}}{p_{2}}=\frac{m_{1}}{m_{2}}\)
As m2 > m1: It follows that p2 > p1. If a ball and a car are travelling with the same velocity, the momentum of the car will be greater than that of the ball. Similarly, we can show that if two objects of same masses are thrown at different velocities, the one moving with the greater velocity possesses greater momentum. Finally, if two objects of masses m1 and m2 are moving with velocities v1 and v2 possesses equal momentum.
m1v1 = m2 v2
\(\frac{v_{1}}{v_{2}}=\frac{m_{2}}{m_{1}}\)
In case m2 > m1 then v2 < v1 i. e, two bodies of different masses possess same momentum, the lighter body possesses greater velocity.
In case m2 > m1 then v2 < v1 i. e, two bodies of different masses possess same momentum, the lighter body possesses greater velocity.
The concept of momentum was introduced by Newton in order to measure the quantitative effect of force.
Momentum of body in term of kinetic energy
Ek = \(\frac{1}{2}\) mv2 ……….. (1)
but p = mv
∴ v = p/m
put in equation (1)
Ek = \(\frac{1}{2} m \frac{p^{2}}{m^{2}}=\frac{p^{2}}{2 m}\)
