The **key difference** between momentum and inertia is that **momentum is a physically calculable property, while we cannot calculate inertia using a formula.**

Inertia and momentum are two concepts in the study of the motion of solid bodies. Momentum and inertia are useful in describing the current state of an object. Both inertia and momentum are concepts that relate to the mass of the object. Moreover, these terms are relativistic variants, which mean the equations for calculating these properties vary when the velocity of the object approaches the speed of light. However, they play a very important role in both Newtonian mechanics (classical mechanics) and relativistic mechanics.

### CONTENTS

1. Overview and Key Difference

2. What is Momentum

3. What is Inertia

4. Side by Side Comparison –Momentum vs Inertia in Tabular Form

5. Summary

## What is Momentum?

Momentum is a vector. We can define it as the product of the velocity and the inertial mass of the object. Newton’s second law mainly focuses on momentum. The original form of the second law states that;

**Force = mass x acceleration**

we can write it in terms of velocity change as:

**Force = (mass x final velocity – mass x initial velocity)/time.**

In a more mathematical form, we can write this as a change of momentum/time. The acceleration described in Newton’s formula is actually an aspect of momentum. It says that the momentum is conserved if no external forces act on a closed system. We can see this in the simple instrument “balance balls”, or Newton’s cradle.

Momentum takes the forms of linear momentum and angular momentum. The total momentum of a system is equal to the combination of linear momentum and angular momentum.

## What is Inertia?

Inertia is derived from the Latin word “iners”, which means idle or lazy. Thus, inertia is a measurement of how lazy the system is. In other words, inertia of a system gives us an idea of how hard it is to change the current state of the system. The higher the inertia of a system, the harder it is to change the velocity, acceleration, direction of the system.

Objects having higher masses have higher inertia. That’s why they are hard to move. Given that it is on a frictionless surface, a moving higher mass object would be hard to stop too. Newton’s first law gives a very good idea about the inertia of a system. It states “an object not subject to any net external force, moves at a constant velocity”. It tells us that an object has a property that is not changed, unless, there is an external force acting upon it. We can also consider an object at rest as an object having null velocity. In relativity, the inertia of an object tends to be infinity when the speed of the object reaches the speed of light. Hence, it requires an infinite force to increase the current velocity. We can prove that no mass can reach the speed of light.

## What is the Difference Between Momentum and Inertia?

Momentum is the product of the velocity and the inertial mass of the object while inertia indicates how hard it is to change the current state of the system. Therefore, the key difference between momentum and inertia is that the momentum is a physically calculable property, while we cannot calculate inertia using a formula. Furthermore, Inertia is just a concept to help us understand and define mechanics better, but momentum is a property of a moving object.

Moreover, while momentum comes in the forms of linear momentum and angular momentum, inertia comes only in one form. Besides, momentum is conserved in some cases. And, we can use this momentum conservation to solve problems. However, inertia doesn’t have to be conserved in any case. Therefore, we can consider this too as a difference between momentum and inertia.

## Summary – Momentum vs Inertia

Inertia is just a concept to help us understand and define mechanics better, but momentum is a property of a moving object. The key difference between momentum and inertia is that momentum is a physically calculable property, while inertia is not.

##### Reference:

1. Jones, Andrew Zimmerman. “Inertia and the Laws of Motion.” ThoughtCo, Jan. 25, 2019, Available here.

##### Image Courtesy:

1. “Newton’s Cradle (15221366308)” By Sheila Sund from Salem, United States – Newton’s Cradle.jpg (CC BY 2.0) via Commons Wikimedia

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