1. What is Angular Momentum?

Angular momentum is a measure of the quantity of rotation of a body, which is conserved in a closed system. It's the rotational analog of linear momentum and depends on the mass, velocity, distance from the rotation axis, and the angle between the velocity and position vectors.

2. How Does the Calculator Work?

The calculator uses the angular momentum formula:

Where:

• \( L \) — Angular momentum (kg·m²/s)
• \( m \) — Mass of the object (kg)
• \( v \) — Linear velocity (m/s)
• \( r \) — Distance from the rotation axis (m)
• \( \theta \) — Angle between velocity and position vectors (degrees)

Explanation: The formula calculates the rotational momentum of an object moving at velocity v at distance r from the rotation axis, considering the angle between these vectors.

3. Importance of Angular Momentum

Details: Angular momentum is fundamental in physics, explaining phenomena from spinning tops to planetary orbits. It's crucial in engineering applications like gyroscopes, satellites, and quantum mechanics.

4. Using the Calculator

Tips: Enter mass in kilograms, velocity in meters per second, radius in meters, and angle in degrees (0-180). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What happens when θ is 90°?
A: At 90°, sin(θ) = 1, giving maximum angular momentum for given m, v, and r values.

Q2: What are typical angular momentum values?
A: Values vary widely - from ~10⁻³⁴ kg·m²/s for electron orbitals to ~10⁴⁰ kg·m²/s for Earth's orbit.

Q3: How is angular momentum conserved?
A: In a closed system with no external torque, total angular momentum remains constant (conservation law).

Q4: What's the difference between L and p?
A: L is angular momentum (rotational), while p is linear momentum (straight-line motion).

Q5: Can angular momentum be negative?
A: Yes, negative values indicate opposite rotational direction based on the right-hand rule convention.