Momentum

Momentum

LEARNING OBJECTIVES
¨    Linear momentum.
¨    Change in linear momentum.
Important Formulae:
1. P= mv                
2. dp =m(v-u)
 
LINEAR MOMENTUM
Consider two balls A and B. Let ball A be heavier than the ball B. i.e. mass (m₁) of ball A is greater than the mass (m₂) of the ball B. Suppose both balls are moving with same velocity \(\overrightarrow v\) . The force require to stop ball A is more than the force required to stop ball B. This shows that the heavier ball has more quantity of motion than the lighter ball. Thus, quantity of motion of a body is directly proportional to the mass of the body.

Now consider two balls of same mass moving with different velocities. The force required to stop the fast moving ball is more than the force required to stop the slow moving ball. So the quantity of motion of the body is directly proportional to the velocity of the ball.

Conclusion :The quantity of motion  of the moving body is proportional to
                (i) mass of the body 
                (ii) velocity of the body.
 This quantity of motion possessed by a moving body is known as momentum of the body. ( or ) The total quantity of motion contained in a body is called momentum.

Mathematical expression : Momentum of a body is equal to the product of the mass (m) of the body and the velocity (\(\overrightarrow V\)) of the body. It is denoted by \(\overrightarrow P\) .
    Thus,    momentum = mass × velocity
                \( \overrightarrow p = m\overrightarrow v \)
momentum is a vector quantity

Note :-  The direction of momentum of a body is same as that of the direction of the velocity of the body.
¨ Units of momentum : S.I. unit of momentum = S.I unit of mass × S.I unit of velocity =kg×m/s
     = kg m/s. Similarly C. G. S. unit of momentum is g cms^–1.
¨ Change of momentum : If ‘u’ and ‘v’ are the initial and final velocity of a body then its, initial momentum = mu  final momentum = mv
    Now change of momentum = final momentum – initial momentum = mv –mu