The **key difference** between acceleration and momentum is that **acceleration refers to the rate of change in velocity of a moving object, whereas the momentum of an object is the product of the mass of the object and its velocity**.

Acceleration is the rate of change of the velocity of an object along with time. Momentum is the product of the velocity and the inertial mass of the object. Both these are vectors having a magnitude and direction.

### CONTENTS

1. Overview and Key Difference

2. What is Acceleration

3. What is Momentum

4. Similarities Between Acceleration and Momentum

5. Side by Side Comparison – Acceleration vs Momentum in Tabular Form

6. Summary

## What is Acceleration?

Acceleration is the rate of change of the velocity of an object along with time. This is a vector having both magnitude and direction. We can get the orientation of an object’s acceleration from the orientation of the net force that acts on the object. Furthermore, we can determine the magnitude of the acceleration through Newton’s second law. The SI unit for the measurement of acceleration is meter per second squared (m/s^{2}).

Concerning the properties of acceleration, the average acceleration of an object over a time period is the change of its velocity that is divided by the duration of the period. Instantaneous acceleration is a form of accelerations where the limit of the average acceleration is over an infinitesimal interval of time. In other words, it is the derivative of the velocity vector with respect to time. Other major forms include centripetal acceleration and centrifugal acceleration, which occur due to forces acting on an object that is moving in a circular path.

## What is Momentum?

Momentum is the product of the velocity and the inertial mass of the object. It is also a vector having both magnitude and direction. 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. There are two main types of momentum as linear momentum and angular 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.

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 is distributed 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.

## What are the Similarities Between Acceleration and Momentum?

- Acceleration and momentum are related to the velocity of a moving object.
- Both are vectors having a magnitude and direction.

## What is the Difference Between Acceleration and Momentum?

Acceleration and momentum are related to the velocity of a moving object. The key difference between acceleration and momentum is that acceleration refers to the rate of change in velocity of a moving object, whereas the momentum of an object is the product of the mass of the object and its velocity.

Below is a summary of the difference between acceleration and momentum in tabular form.

## Summary – Acceleration vs Momentum

Both acceleration and momentum are vectors having a magnitude and direction. The key difference between acceleration and momentum is that acceleration refers to the rate of change in velocity of a moving object, whereas the momentum of an object is the product of the mass of the object and its velocity.

##### Reference:

1. Jones, Andrew Zimmerman. “How to Define Acceleration.” ThoughtCo, Aug. 27, 2020, Available here.

##### Image Courtesy:

1. “Acceleration as derivative of velocity along trajectory” By Fred the Oyster (CC BY-SA 4.0) via Commons Wikimedia

2. “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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