## Main Difference – Inertia vs. Momentum

The terms inertia and momentum can both be used to describe how difficult it is to change the state of motion of an object. The **main difference** between inertia and momentum is that **inertia does not depend on the object’s velocity**, whereas **momentum depends on the object’s velocity**.

## What is Inertia

Inertia is a term that describes **the resistance of an object to change its velocity**. This includes the resistance shown by the objects at rest to start moving, and the resistance by a body in motion to change its speed and/or its direction of motion. Inertia is usually characterized by a body’s mass. It is more difficult to change the state of motion of more massive objects, so they have more inertia.

When a bus suddenly applies brakes, the passengers may get “thrown” forward. Here, the bus has not exerted a forward force on the passengers! Instead, this is an effect of inertia. If passengers are not making enough contact with the bus, a sufficient force cannot be applied on the passengers to *change* their state of (forward) motion, and so they will try to keep moving at the same speed in a straight line.

Another famous trick that utilizes inertia is pulling out a tablecloth from under objects on a table without making them fall off. Here, the objects on the table tend to stay where they are due to inertia. When the cloth is pulled swiftly downwards, not enough force can be exerted on the objects to change their state of rest:

## What is Momentum

Momentum is simply defined for an object as the product of the object’s mass and velocity. Since the mass of an object is an indication of the object’s inertia, depends on an object’s inertia. The resultant force on an object can be given by the rate of change of momentum of the object. In this sense, an intuitive interpretation for momentum could be, “*the amount of force required to bring a moving object to rest in one second*“. Note that momentum depends on the state of motion, whereas inertia does not. An object at rest will have inertia, whereas it will not have a momentum.

Momentum is an extremely important concept for physics. According to the **law of conservation of momentum**, the total momentum of a system of objects will remain constant as long as no external forces are applied on the system. You might see players in cricket swing their arms back as they catch the ball. This is because when their hand is also moving in the direction of the ball, the change in momentum for the ball is small, and so the force exerted on the hand by the ball is also smaller. Conservation of momentum can be demonstrated using a Newton’s cradle (shown below).

## Difference Between Inertia and Momentum

### Dependence on Speed

**Inertia** is indicated only by an object’s mass.

**Momentum** depends on an object’s mass as well as velocity.

### Calculation

**Inertia** is a qualitative concept and has no specific mathematical definition that allows for it to be calculated.

**Momentum** is defined as the product of an object’s mass and velocity.

**Image Courtesy**

“Pendule en mouvement – Newton’s cradle” by hellolapomme (Own work) [CC BY-SA 2.0], via flickr