# Linear Momentum vs. Angular Momentum: What's the Difference?

Edited by Aimie Carlson || By Janet White || Published on December 19, 2023
Linear momentum is the product of mass and velocity of an object in motion, while angular momentum is the rotational equivalent, dependent on the object's rotational velocity and moment of inertia.

## Key Differences

Linear momentum describes the motion of an object along a straight path. Angular momentum characterizes rotational motion.
Linear momentum is a vector quantity, indicating both the magnitude and direction of an object's motion. Angular momentum, also a vector quantity, represents the angular motion of an object and its rotational direction.
Conservation laws apply to both; linear momentum is conserved in a system with no external forces, while angular momentum is conserved in a system with no external torques.
Linear momentum is primarily influenced by mass and linear velocity. Angular momentum depends on the distribution of an object's mass (moment of inertia) and its rotational speed.
In collisions, linear momentum helps calculate the motion post-collision. In rotational dynamics, angular momentum helps understand spinning objects' behavior, like gyroscopes or planets.

## Comparison Chart

### Definition

Product of mass and linear velocity
Product of moment of inertia and angular velocity

### Type of Motion

Straight-line motion
Rotational or spinning motion

### Conservation Law

Conserved in absence of external forces
Conserved in absence of external torques

### Dependent Factors

Mass and velocity of the object
Object's distribution of mass and rotational speed

## Linear Momentum and Angular Momentum Definitions

#### Linear Momentum

Dependent on the object’s mass and its velocity.
A train, due to its large mass, carries a huge amount of linear momentum even at low speeds.

#### Angular Momentum

Conserved in a system with no external torques, a fundamental principle in rotational dynamics.
Earth maintains its angular momentum, causing consistent rotational periods and seasons.

#### Linear Momentum

A vector quantity, indicating both the magnitude and direction of motion.
The linear momentum of a car determines its impact force in a collision.

#### Angular Momentum

Key in understanding the behavior of rotating systems, from atoms to galaxies.
The angular momentum of planets around the sun explains their stable orbital paths.

#### Linear Momentum

Integral in understanding the dynamics of collisions and interactions.
In a car crash, the linear momentum before and after the impact is crucial for analysis.

#### Angular Momentum

A vector quantity, indicating both the magnitude and direction of rotational motion.
The angular momentum of a spinning top determines how long it can spin before toppling.

#### Linear Momentum

The quantity of motion of a moving body, measured as a product of its mass and velocity.
A speeding bullet has significant linear momentum due to its high velocity and mass.

#### Angular Momentum

Dependent on an object's distribution of mass and its rotational speed.
A discus thrown by an athlete has a significant angular momentum due to its spin and mass distribution.

#### Linear Momentum

Conserved in an isolated system where external forces are absent.
In space, an astronaut's linear momentum remains constant without external forces.

#### Angular Momentum

A measure of the amount of rotation an object has, taking into account its velocity and moment of inertia.
A figure skater increases her angular momentum by pulling her arms close to her body while spinning.

## FAQs

#### Can linear momentum change?

Yes, it changes when an external force is applied to the object.

#### What affects angular momentum?

Changes in rotational speed, direction, or an object's moment of inertia.

#### How is angular momentum defined?

Angular momentum is the rotational equivalent of linear momentum, depending on rotational speed and moment of inertia.

#### Is angular momentum conserved?

Yes, in the absence of external torques, it's conserved.

#### What role does the moment of inertia play in angular momentum?

It's crucial; larger moments of inertia result in larger angular momenta for the same angular velocity.

#### What is linear momentum?

It's the product of an object's mass and its velocity.

#### Is linear momentum a scalar or a vector?

It's a vector, having both magnitude and direction.

#### How do mass and velocity affect linear momentum?

Increased mass or velocity results in greater linear momentum.

#### How is angular momentum useful in astronomy?

It helps understand planetary motions and the behavior of galaxies.

#### What units are used for linear momentum?

It's measured in kilogram-meters per second (kg·m/s).

#### Does linear momentum depend on the frame of reference?

Yes, it varies with different frames of reference.

#### Is angular momentum frame dependent?

Yes, like linear momentum, it's also frame-dependent.

#### Can linear momentum be transferred?

Yes, like in collisions where momentum is transferred between objects.

#### Why is linear momentum important in sports?

It's crucial for understanding motion and impacts in various sports.

#### How is linear momentum used in vehicle safety design?

It helps in designing crumple zones and understanding impact forces during crashes.

#### What are the units for angular momentum?

Angular momentum is measured in kilogram-meters squared per second (kg·m²/s).

#### How does angular momentum affect a gyroscope?

It keeps the gyroscope stable and upright due to its conservation.

#### What happens to angular momentum when a dancer pulls in their arms?

It increases, causing the dancer to spin faster.

#### Can angular momentum be zero?

Yes, if there's no rotation or if moment of inertia is zero.

#### Can two objects have the same linear momentum?

Yes, if their mass-velocity products are equal.