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.

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:

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

where,

• • \( \vec{L} \) 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:

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

where,

• \( \vec{L} \) 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 +…+ l_n

Solved Examples on Angular Momentum Formula

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