Momentum

Momentum is defined as the tendency of a body to keep moving in the same direction unless an external force acts on the body. Momentum is basically the multiplication of the mass and velocity of the body. Momentum has both magnitude as well as direction hence it is a vector quantity. It means momentum has magnitude and direction.

There is also a part which will be most required for studying momentum, that is, elastic collision. Elastic collision is collision in which two objects collide and energy is transferred from one object to the other, but there is no net loss of kinetic energy. For example, two balls of the same type move towards each other at the same speed. They collide and bounce off each other without losing speed. This collision is an ideal case since no energy was lost.

Momentum Formula

The momentum formula is given as

Here, 

p = momentum

m= mass of body

v = velocity of body

Types of momentum

Linear Momentum

The momentum of a body which moves in a straight line is termed as Linear Momentum.

The linear momentum formula is as follow

p=m×v

Angular Momentum

The momentum of a body which moves at an angle is termed as angular momentum. In angular momentum, the mass of the object is the same but velocity is replaced with angular velocity.

This makes a change in the equation of momentum. Angular momentum is also generated when a body spins on its axis. 

The angular momentum formula is

L=m×v×r

L= Angular momentum

r= radius 

m= mass of body

v= velocity of body

Momentum without Mass

We have already discussed that momentum depends on mass and velocity of a body. If either of these two values ​​is zero, then the value of momentum is also zero. However, there is one exception: light. Light has no mass but has momentum. We don’t see things falling when light hits them because the momentum of light is small, but it can be measured. In fact, for photons (the smallest particles of light), the energy E and momentum p are related by the following equation:

E=p×c

Here, 

c= speed of light

E= energy

p= momentum

The momentum of light is very small as we do not notice it in daily life. But it’s big enough to be measurable and even usable. Example In optical traps, the momentum of light is used to catch and manipulate minute objects.

Inertia

Inertia is the resistance of a physical body/object to a change in its velocity. This includes the changes to the object’s speed, or in the direction of motion of the body. One aspect of this property is the tendency of objects to move in a straight line at constant speed when no force is acting on them.

Moment of Inertia

The moment of inertia is defined as the quantity expressed by the body resisting angular acceleration, which is the sum of the product of the mass of each particle and the square of it’s distance from the axis of rotation of an object. Or, more simply put, it can be described as a quantity that determines the amount of torque required for a given angular acceleration on an axis of rotation. The SI unit is Kg.m2

The moment of inertia is

I=m×r2

Here, 

m = Summation of product of the mass.

r = distance.

I = Moment of Inertia.

Newton’s Second Law

According to the Newton’s Second Law “the force acted on an object is always equals to the product of mass and acceleration of that object.”

Hence the force is

F=m.a

Here,

F = force

m = mass

a = acceleration

Importance of momentum

Momentum determines the force required to stop objects and keep them moving. For example, momentum explains that it takes more force to stop an object with a higher momentum than an object with a lower momentum. Therefore, momentum is an important factor which is considered while designing systems to stop a body which is in motion.

Momentum is also used to predict the direction and speed of motion of objects after their collision.

Conclusion

Momentum is defined as the tendency of a body to keep moving in the same direction unless an external force acts on the body. Momentum is basically the multiplication of the mass and velocity of the body. Momentum has both magnitude as well as direction hence it is a vector quantity. It means momentum has magnitude and direction.

The momentum formula is given as

p=mv

The moment of inertia is

I=m×r2

According to the Newton’s Second Law, the force is given as

F=ma

The energy E and momentum p of photon are related by the following equation:

E=p x c