Magnitude of Angular Momentum Formula

Angular Momentum Formulas:

\[ L = I \omega \quad \text{or} \quad L = m v r \sin\theta \]

Calculation Type:

Moment of Inertia (I):

kg·m²

Angular Velocity (ω):

rad/s

Angular Momentum (L):

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1. What is Angular Momentum?

Angular momentum is a measure of the quantity of rotation of a body, representing the rotational equivalent of linear momentum. It is conserved in isolated systems where no external torques act.

2. Angular Momentum Formulas

The calculator provides two approaches to calculate angular momentum:

\[ \text{Rotational: } L = I \omega \] \[ \text{Linear: } L = m v r \sin\theta \]

Where:

\( L \) — Angular momentum (kg·m²/s)
\( I \) — Moment of inertia (kg·m²)
\( \omega \) — Angular velocity (rad/s)
\( m \) — Mass (kg)
\( v \) — Linear velocity (m/s)
\( r \) — Radius or lever arm (m)
\( \theta \) — Angle between velocity and radius vectors (degrees)

Explanation: The rotational formula applies to rotating rigid bodies, while the linear formula applies to point masses moving in curved paths.

3. Applications and Importance

Details: Angular momentum is fundamental in understanding rotational dynamics, celestial mechanics, quantum physics, and engineering applications like gyroscopes, satellites, and rotating machinery.

4. Using the Calculator

Tips: Select calculation type first. For rotational calculation, enter moment of inertia and angular velocity. For linear calculation, enter mass, velocity, radius, and angle. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between rotational and linear angular momentum?
A: Rotational angular momentum describes spinning objects, while linear angular momentum describes objects moving in curved paths relative to a point.

Q2: When is angular momentum conserved?
A: Angular momentum is conserved when no external torque acts on the system. This principle is crucial in many physical phenomena.

Q3: What is moment of inertia?
A: Moment of inertia measures an object's resistance to changes in rotation, depending on mass distribution relative to the axis of rotation.

Q4: Why is the angle important in the linear formula?
A: The angle determines the component of velocity perpendicular to the radius vector, which contributes to angular momentum.

Q5: What are typical units for angular momentum?
A: Standard SI units are kg·m²/s, though other systems may use different units like g·cm²/s.