# Momentum and Impulse

## Newton’s Second Law of Motion – Momentum

Newton introduced the concept of momentum to explain the measurement of force impressed on a body. The momentum, also known as linear momentum, is defined as the total quantity of motion possessed by the moving body. It is measured as the product of mass and velocity. The linear momentum is expressed by the equation

p = mv

Here, p is the momentum

m is the mass of the body

v is the velocity of the body

Momentum is a vector quantity. The direction of momentum is along the direction of the velocity v of the body. The S.I unit of momentum is kgm/s

When forces of the same magnitude are made to act on two bodies with different masses or the same interval of time, the lighter object will move with more velocity than the heavier object. However, the change in the momentum of both objects will be the same. This led to Newton’s second law of motion. The law states that “The time rate of change of momentum of a body is directly proportional to the force impressed and it takes place in the direction of the applied force”.

## Impulse and Impulsive force

If a large force is applied for a very short interval of time, it produces a finite change in the momentum. In such a situation, neither the force nor the time interval can be measured. However, the effect caused by the body .i.e., the change in the momentum can be determined.

According to Newton’s second law of motion,

F = ma = m (v – u)/t

Ft = mv – mu = change in momentum

Here m is the mass of the body

a is the acceleration, it is the change in velocity with respect to time

v is the final velocity of the body

u is the initial velocity

t is the time for which the force is applied

The product of force and time (Ft)  is called the impulse, meaning the total effect of the force. The force itself is called the impulsive force. Therefore, the impulsive force is a very large force that acts for a very short interval of time and causes a finite change in the momentum. Impulseis a vector quantity. The direction of the impulse is along the direction of the force. The S.I unit for force is Newton seconds (Ns).

## Application of Impulse

• A cricketer lowers his hands to catch a fast-moving ball. This is to reduce the force exerted by the ball on the hands by increasing the time of catch. As a result, the cricketer doesn’t hurt his hand while catching the ball.
• The automobiles are provided with a spring system to reduce the damage to the vehicle.
• A person falling on a hard surface gets hurt more than a person falling on a bed.
• To avoid breakage glasswares are usually wrapped with straw
• When the vehicles go out of control it is advised to strike something soft to reduce the damage.