Angular Momentum Formula

Angular Momentum Formula

Momentum is calculated as the product of an object’s mass and velocity. Any object with mass has momentum. The sole distinction in angular momentum is that it applies to rotating or spinning objects. Is this the rotating equivalent of linear momentum?

Angular Momentum

If you try to ride a bicycle without a kickstand, you will most likely fall off. But as you start cycling, these wheels gain angular momentum. They will resist change, making balance simpler.

Angular momentum is defined as follows:

Any rotating object’s moment of inertia multiplied by its angular velocity.

It is the attribute of a spinning body determined by the product of its moment of inertia and angular velocity. It is a vector quantity, therefore the direction, as well as the magnitude, are taken into account.

Symbol The angular momentum is a vector quantity, denoted by

Units It is measured using SI base units: Kg.m2.s-1
Dimensional formula The dimensional formula is: [M][L]2[T]-1

Angular Momentum of a Single Particle

Angular momentum can be experienced by a single particle when the object is accelerating around a fixed position. For example, in case of the earth and the sun. Earth is revolving around the sun in its orbit, where the sun is fixed at its position.

Angular momentum, in that case is given by the formula:

\( \vec{L} = r \times \vec{p} \)


    • \( \vec{L} \) is Angular Momentum
    • \( r \) is Radius of Rotational Path
    • \( \vec{p} \) is Linear Momentum of Object

Angular Momentum for Extended Object

Angular momentum can be experienced by a point object when the object is rotating about a fixed position. For example, in case of the earth rotating at its axis.

Angular Momentum, in that case is given by the formula:

\vec{L} = I \times \vec{\omega}


  • \( \vec{L} \) is Angular Momentum
  • \( I \) is Rotational Inertia
  • \( \vec{\omega} \) is Angular Velocity of Object

The angular momentum of a system of particles

The angular momentum of a system of particles is the vector sum of the individual angular momentum of each particle. The angular momentum of a particle is calculated as l = r×p, where r represents the particle’s distance from the origin. where p is the particle’s linear momentum. The angular momentum of the system with n particles is,

L = l1 + l2 + l3 +…+ ln

Solved Examples on Angular Momentum Formula

Students frequently question how to properly use the Extramarks’ Angular Momentum Formula tools. Teachers at Extramarks offer advice on how to use their Angular Momentum Formula resources as a reference. Students frequently encounter doubts that impede their progress as they attempt to solve the chapter’s problems for the first time. Students typically wait until someone else clarifies their doubts.

Therefore, Extramarks’ Angular Momentum Formula tools offer assistance whenever and wherever needed. Students can immediately consult the Angular Momentum Formula tools provided by Extramarks whenever they have any questions. Students can determine which sections need revision by reading through the resources and identifying the cause of their doubt. Pupils can determine the kinds of answers that different boards are looking for from their students by using the information on the Angular Momentum Formula made available by Extramarks. Students benefit greatly from the resources because they can get them from any location. These answers can be found on the Extramarks website as well as through their mobile app.

Physics Related Formulas
Acceleration Formula Rotational Kinetic Energy Formula
Power Formula Wave Speed Formula
Velocity Formula Voltage Divider Formula
Average Speed Formula Static Friction Formula
Momentum Formula Average Force Formula
Pressure Formula Banking Of Road Formula
Torque Formula Deceleration Formula
Displacement Formula Drag Force Formula
Kinetic Energy Formula Elastic Collision Formula
Potential Energy Formula Electrical Resistance Formula

FAQs (Frequently Asked Questions)

1. What is Angular Momentum?

Angular momentum is defined as the product of Moment of Inertia and Angular Velocity of any Rotating Object.

2. Is Angular Momentum is Scalar or Vector Quantity?

Angular Momentum has both magnitude and direction, therefore it is a Vector Quantity.

3. Is Angular Momentum Always Conserved?

No, Angular momentum is conserved only when no net external torque is applied to rotating body.