1. What is Angular Momentum?

Angular momentum is a vector quantity that represents the rotational equivalent of linear momentum. It describes the quantity of rotation of a body and is conserved in a closed system. The angular momentum vector (L) is calculated as the cross product of the position vector (r) and the linear momentum vector (p).

2. How Does the Calculator Work?

The calculator uses the cross product formula:

Which in component form is:

• \( L_x = r_y p_z - r_z p_y \)
• \( L_y = r_z p_x - r_x p_z \)
• \( L_z = r_x p_y - r_y p_x \)

Explanation: The cross product produces a vector perpendicular to both r and p, with magnitude equal to the product of their magnitudes and the sine of the angle between them.

3. Importance of Angular Momentum

Details: Angular momentum is fundamental in physics, governing rotational motion in systems from atomic particles to galaxies. Conservation of angular momentum explains phenomena like ice skaters spinning faster when pulling in their arms.

4. Using the Calculator

Tips: Enter all components of the position vector (in meters) and momentum vector (in kg·m/s). The calculator will compute each component of the angular momentum vector (in kg·m²/s).

5. Frequently Asked Questions (FAQ)

Q1: What's the right-hand rule for angular momentum?
A: Point fingers in direction of r, curl toward p; thumb points in L direction. This shows the perpendicular nature of angular momentum.

Q2: How is angular momentum different from torque?
A: Torque is the rotational equivalent of force (change in angular momentum over time), while angular momentum is the rotational equivalent of linear momentum.

Q3: When is angular momentum conserved?
A: In closed systems with no external torque, total angular momentum remains constant, though it may be redistributed within the system.

Q4: What are typical units for angular momentum?
A: SI units are kg·m²/s, but atomic physics often uses reduced Planck constant ħ (1.05×10⁻³⁴ J·s) as a natural unit.

Q5: How does angular momentum relate to moment of inertia?
A: For rigid bodies, L = Iω where I is moment of inertia and ω is angular velocity, analogous to p = mv for linear motion.