# Momentum of Inertia

The study of causes of motion of bodies is called Dynamics. While studying the motion of bodies we treat bodies like particles and we do not consider the effects of distant objects on the motion of such particles. The study of the motion of bodies moving at speeds that are very small compared to 'c' the speed of light is called classical mechanics. In such a study we apply Newton's laws of motion.

In earlier times, motion of bodies was studied by philosophers. Most philosophers believed that a body moved with uniform velocity due to some external agent. They also thought that if there were no external agent the body would naturally come to rest. Galileo was the first to show that some external force was necessary to change the velocity of a body but that no external force was necessary to maintain the velocity of a body. This principle was adopted by Newton in his first law of motion.

## Momentum of Inertia : Definition of Inertia

Inertia is defined from newton's first law of motion. " Every body continues in its state of rest of of uniform motion in a straight line unless it is acted upon by a net external force " .     The law enables us to define inertia and force. From this law it can be concluded that if the net external force on an object is zero, the acceleration of the object is zero.

Inertia : If the net external force is zero, a body at rest continues to be at rest and a body in motion continues to move with uniform velocity. This property is called inertia. It is the resistance to change the state of uniform motion. Mass is a measure of inertia.

Some examples of inertia:

1) When we are in a bus that starts suddenly, our feet in touch with the floor would be accelerated by the frictional force to move along with the bus if the acceleration of the bus is moderate. While our feet go with the bus, the rest of the body remains where it is due to inertia of rest i.e., we fall backwards.

2) when the bus stops suddenly our feet stop due to the friction. But the rest of the body continues to move forward due to inertia of motion.

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## Momentum of Inertia : Definition of Momentum

By Newton's second law of motion we can learn about the motion of a body when there is a net external force on the body. The second law gives the relation between the net external force and the acceleration of the body. The motion of a body is represented by two physical quantities in dynamics. One of them is momentum and the other is kinetic energy.

Momentum :  When two stones of different masses fall from the same height on a vehicle, which will cause greater damage ? Obviously the larger stone causes greater damage since the larger stone with greater mass applies greater force even though both stones have same velocity. If two stones of same mass fall from two  different heights fall on a vehicle which causes greater damage ? The stone from greater height produces greater damage because the stone falling from a greater height will have larger velocity and it applies greater force. Two stones of different masses are dropped from different heights on a vehicle. The stone of larger mass dropped from greater height causes greater damage since its product of mass and velocity is larger. Thus, a physical quantity which is the product of mass and velocity is related to force . Such a physical quantity is called momentum .

Momentum of a body is defined as a product of the mass and velocity of the body. It is denoted by p.

If the mass of a body is m and its velocity is v then its momentum is   p = mv.  Its SI unit is kg ms-1 and dimensional formula is [MLT-1]. It is a vector quantity whose direction is in the direction of velocity since it is a scalar multiple of a vector.

i.e., p = mv

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