How momentum exists in our daily routine?

Let us consider an example for explaining the concept of momentum. You might have seen many road accidents. Some are minor, and some are significant accidents. The severity of the resulting damage is according to the speed of the vehicle.

 

This is because the momentum of cars running at high speeds is very high and that causes damages to the vehicles and injuries to passengers during the collision. Then what is momentum? The momentum of the body is defined as the product of its mass and velocity. Momentum is a vector quantity and takes place in the direction of acceleration. The SI unit is kilogram metres per second or kgms-1.

Momentum = mass x velocity

Or, p = m × v

Where p = momentum

m= mass

v= velocity or speed

Types of momentum

There are mainly two types of momentum: Angular and linear momentum.

Angular momentum

The angular momentum is the inertia of rotation motion. This momentum is the same at every point of an orbit.  When it is closer, it increases speed. Angular momentum is obtained by multiplying a body’s mass by its angular velocity. The angular momentum of a rigid object is defined as the product of the moment of inertia and the angular velocity.

Angular momentum is a vector quantity. It is derivable from the expression for the angular momentum of a particle

L = I × ѡ

Where I = Moment of inertia

ѡ = Angular velocity

How to find the direction of angular momentum and angular velocity?

By using the right hand thumb rule, the direction of angular momentum and angular velocity can be found. Both L and ω are vectors. Because angular momentum is related to angular velocity by L = I ω. The direction of L is the same as the direction of ω. This rule says that the fingers on your hand curl towards the direction of rotation or force exerted, and your thumb points towards the direction of angular momentum, torque, and angular velocity.

Linear momentum,

Linear momentum is defined as the product of a system’s mass multiplied by its velocity. It is the quantity of mass associated with a body that moves along a straight path. It is a vector quantity that is the product of the mass of an object and its velocity. Any change in the mass or the velocity of the system causes a change in linear momentum.

Conservation of Momentum

The momentum of a system is constant if there is no external force acting on the system. For a collision between two objects in an isolated system, the total momentum of the two things before the collision is equal to the total momentum of the two objects after the collision.

Derivation:

Consider a truck and a car moving fast, and a truck collides with the car accident. Now the momentum lost by the truck is gained by the car.

Mass of the truck = m1

Velocity = u1

The momentum of the truck = m1u1

Mass of the car = m2

Velocity = u2

The momentum of the car = m2u2

The Collision time = t

The velocity of both the vehicles change at the time of the collision and become v1 and v2. The mass remains unchanged.

Hence, now the total momentum = m1v1 + m2v2

Acceleration of car (a) = (v2–u2)/t

Also, F = ma

F1  = Force exerted by truck on the car

F1 = m2(v2–u2)/t

Acceleration of truck =(v1–u1)/t

F2  =   m1(v1–u1)/t and F1 = –F2

m2(v2– u2)/t = –m1(v1– u1)/t

m2v2–m2u2 = –m1v1+m1u1

or m1u1+m2u2  = m2v2+m1v1

Application of momentum in daily life

1. Suppose we run every day. This causes momentum, and if the running is not consistent, then a negative momentum is built, which makes it even harder to get started.
2. While doing karate, a player breaks a piece of the ice slab using his single hand. The considerable momentum of the fast-moving hand is reduced to zero in a very, very short time. Thus, it exerts a massive force on the ice slab, which is sufficient to break them apart.
3. The momentum of vehicles running at high speeds is very high and causes a lot of damage to passenger’s cars and injuries during the collision.

Summary

• The momentum of the body is defined as the product of its mass and velocity.
• Law of Momentum:: The applied resultant force acting on an object is equal to the rate of change of the object’s momentum, and this force is in the direction of the change in momentum.
• The angular momentum is the inertia of rotation motion. The right-hand thumb rule can determine the direction.
• Linear momentum is defined as the product of a system’s mass multiplied by its velocity.
• Momentum has a lot many real-life examples, like a collision of two vehicles which causes momentum.