What is Inertia?

Inertia of a body is the tendency of the body to remain in its original state. If a body is at rest initially, it always remains at rest until a net force is applied to it. The tendency of a body to remain at rest is called inertia of rest.

Likewise, if a body is in motion, it always wants to be in motion until a net force is applied to it. The tendency of a body to remain in motion is called inertia of motion.

In other words if no net force is applied to a body at rest, the body will always be in the state of rest and if no net force is applied to a body in motion, it'll always move with constant velocity (never stops until a net force acts on it).

Inertia of a body is the tendency of that body to resist the change in its current state either at rest or in motion.

A coin is over a paper. When you suddenly pull the paper towards you with high speed, the coin falls back to the original place where it was initially; the coin didn't come with the paper towards you but instead it wanted to remain in its original place at rest. This indicates that the coin resists to come in motion with the paper. This tendency of the coin at rest to resist to come in motion is the inertia of rest.

A bus example is very familiar and easy to understand inertia. A bus is moving with constant velocity with some passengers. Initially the passengers are also moving with the same velocity in the bus but when driver applies breaks to stop the bus, the passengers move forward.

The reason behind this is, the passengers were initially in motion and when the bus stops the passengers tend to be in motion due to the inertia of motion and move forward. Now the bus is stopped and the passengers and the bus are both at rest. When the driver accelerates the bus, the passengers move backwards. Initially the passengers were at rest and when the bus accelerates the passengers still want to be at rest due to the inertia of rest and move backwards.

The forward or backward movement of your body becomes more clear when you understand inertial frame of reference. When viewed from inside the bus, it may seem weird that you are moving without any force applied on you. Inertia is the heart of Newton's first law of motion and we also call the Newton's first law of motion as the law of inertia.

Mechanics
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