The **key difference** between linear momentum and angular momentum is that **the term linear momentum describes an object moving in a direct path whereas the term angular momentum describes an object with angular motion.**

Angular momentum and linear momentum are two very important concepts in mechanics. These two concepts play a vital role in most of the fields in dynamics.

### CONTENTS

1. Overview and Key Difference

2. What is Linear Momentum

3. What is Angular Momentum

4. Side by Side Comparison – Linear Momentum vs Angular Momentum in Tabular Form

5. Summary

## What is Linear Momentum?

Linear momentum is a very important property of a moving object. We can use the term linear momentum to describe an object moving on a direct path. The momentum of an object is equal to the mass of the object multiplied by the velocity of the object (p =mv). Since the mass is a scalar, the linear momentum is a vector, which has the same direction as the velocity.

One of the most important laws regarding momentum is Newton’s second law of motion. It states that the net force acting on an object is equal to the rate of change of momentum. Since mass is a constant on non-relativistic mechanics, the rate of change of linear momentum is equal to mass multiplied by the acceleration of the object (μ = ma).

The most important derivation from this law is the linear momentum conservation law. This states that if the net force on a system is zero, the total linear momentum of the system remains constant. Moreover, linear momentum is conserved even in relativistic scales. Furthermore, the linear momentum depends on both the mass of the object and the space-time coordinate change of the object.

## What is Angular Momentum?

Angular momentum describes an object with angular motion. To define the angular momentum, one must first know what the moment of inertia is. The moment of inertia of an object is a property that depends on both the mass of the object and the mass distribution from the place that we measure the moment of inertia. If the total mass distributes closer to the rotational axis, the moment of inertia is lower. However, if the mass spreads out far from the axis, the moment of inertia is higher.

Angular momentum of an object is the product of the moment of inertia and the angular velocity of the object (L = Iω). Angular velocity is a vector. We can determine the direction of the angular velocity by the right-hand corkscrew law. Since the moment of inertia is a scalar, angular momentum is a vector, with a direction perpendicular to the plane of rotation that we can decide by the right-hand corkscrew rule. To change the angular momentum of a system we must apply an external torque. The rate of change of angular momentum is proportional to the torque we apply. If there is no external torque, the angular momentum of a closed system is conserved.

## What is the Difference Between Linear Momentum and Angular Momentum?

Linear momentum is the product of a system’s mass multiplied by its velocity while angular momentum is the rotational equivalent of linear momentum. The key difference between linear momentum and angular momentum is that the term linear momentum describes an object moving in a direct path whereas the term angular momentum describes an object with angular motion.

The unit of measurement of linear momentum is kgm/s while the unit of measurement of angular momentum is kgm^{2}rad/s. So, this is also a significant difference between linear momentum and angular momentum. Moreover, the equation of linear momentum is p =mv where p is linear momentum, m is the mass of the moving object and v is the velocity of motion. Whereas, the equation of angular momentum is L = Iω where L is angular momentum, I is the moment of inertia and ω is the angular velocity.

## Summary – Linear Momentum vs Angular Momentum

In brief, linear momentum and angular momentum are important concepts in physics to describe the motion of an object. The key difference between linear momentum and angular momentum is that the term linear momentum is applied for an object moving in a direct path whereas the term angular momentum is applied for an object with angular motion.

##### Reference:

1. “Angular Momentum.” Wikipedia, Wikimedia Foundation, 23 May 2019, Available here.

2. Richmond, Micheal. “Linear Momentum.” Available here.

##### Image Courtesy:

1. “Change-in-angluar-speed-due-to-change-in-moment-of-inertia” By MikeRun – Own work (CC BY-SA 4.0) via Commons Wikimedia

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