Angular Momentum

In our daily life, we often see things spinning or rotating — like a spinning top, a turning wheel, or even the Earth itself. These spinning motions follow the laws of physics, and one of the most important concepts behind them is called angular momentum. Just like how objects moving in a straight line have momentum, rotating or spinning objects have angular momentum. It tells us how much rotation an object has and how hard it would be to stop that rotation.

To understand this better, let’s take an example. Imagine a figure skater spinning on ice. When the skater pulls their arms close to their body, they start spinning faster. This happens because their angular momentum is conserved — it remains the same before and after they move their arms. This is a great example of how angular momentum works and how important it is in explaining the motion of rotating objects.

So, what is angular momentum? In simple words, it is the quantity of rotational motion an object has. It depends on how much mass the object has, how fast it is spinning, and how far the mass is from the center of rotation. When these three things come together, they form what we call angular momentum.

Understanding angular momentum helps us explain many things — from why Earth keeps spinning without stopping to how planets stay in orbit around the Sun. It also plays a big role in designing machines, engines, and even space rockets.

Do Check: Zener Diode

In this article, we will explore everything you need to know about angular momentum, including its definition, formula, units, dimensions, real-life examples, and the law of conservation of angular momentum — all explained in a simple and easy way.

Angular Momentum Definition

Angular momentum is the quantity of rotation of an object and is a product of its moment of inertia and angular velocity. In simpler words, if something is spinning or rotating, it has angular momentum.

Angular Momentum Formula

The basic angular momentum formula is:

L = I × ω

• L is the angular momentum
• I is the moment of inertia
• ω is the angular velocity

For a point mass:

L = m × r × v

The angular momentum is the product of the moment of inertia and angular velocity or the cross product of position vector and linear momentum.

Units and Dimensions

Angular Momentum Units

The SI unit of angular momentum is kg·m²/s.

Dimensional Formula of Angular Momentum

The dimensional formula of angular momentum is:

[M¹L²T⁻¹]

This represents the angular momentum dimension or dimension of angular momentum.

Do Check: Reflection of Light

Types of Angular Momentum

Orbital Angular Momentum

Orbital angular momentum occurs when an object revolves around a point or axis.

Orbital Angular Momentum Formula

L = m × r × v

This is the basic orbital angular momentum formula.

Angular Momentum of Electron

The angular momentum of electron in atomic physics is given by:

L = n × ħ

Where n is the principal quantum number and ħ is the reduced Planck's constant.

Law of Conservation of Angular Momentum

Conservation of Angular Momentum

This law states that if no external torque acts on a system, the total angular momentum remains constant.

Example: When a figure skater pulls in their arms, they spin faster because angular momentum is conserved.

I₁ × ω₁ = I₂ × ω₂

Relation Between Torque and Angular Momentum

Just like force changes linear momentum, torque changes angular momentum.

Torque (τ) = dL/dt

This is the relation between torque and angular momentum.

Do Check: Human Eye

Factors Affecting Angular Momentum

• Mass of the object
• Distance from the axis
• Speed or velocity

So, orbital angular momentum depends on mass, radius, and velocity.

Applications of Angular Momentum

• Astronomy: Explains planetary orbits.
• Sports: Used by skaters and gymnasts.
• Electronics: Helps in understanding atomic structure.
• Engineering: Used in turbines and flywheels.

Real-Life Examples

• A spinning wheel continues to rotate unless torque is applied.
• A dancer spins faster when arms are pulled in (due to conservation of angular momentum).
• Planets maintain their orbits due to constant orbital angular momentum.

Do Check: Anemometer

Conclusion

Understanding angular momentum is essential in physics. It helps explain rotation in daily life, nature, and technology. The angular momentum formula, conservation of angular momentum, and angular momentum units are foundational concepts that build a strong physics base.