Angular Momentum Calculator Vector

Angular Momentum Vector Formula:

\[ \vec{L} = \vec{r} \times \vec{p} \]

Position Vector X-component (r_x):

Position Vector Y-component (r_y):

Position Vector Z-component (r_z):

Linear Momentum X-component (p_x):

kg·m/s

Linear Momentum Y-component (p_y):

kg·m/s

Linear Momentum Z-component (p_z):

kg·m/s

Angular Momentum Vector X-component (L_x):

Angular Momentum Vector Y-component (L_y):

Angular Momentum Vector Z-component (L_z):

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1. What is Angular Momentum Vector?

Angular momentum is a vector quantity that represents the rotational equivalent of linear momentum. It describes the rotational inertia and rotational velocity of an object about a particular axis.

2. How Does the Calculator Work?

The calculator uses the cross product formula:

\[ \vec{L} = \vec{r} \times \vec{p} \]

Where:

\( \vec{L} \) — Angular momentum vector (kg·m²/s)
\( \vec{r} \) — Position vector from axis of rotation (m)
\( \vec{p} \) — Linear momentum vector (kg·m/s)

Explanation: The cross product operation ensures the angular momentum vector is perpendicular to both the position and linear momentum vectors, following the right-hand rule.

3. Importance of Angular Momentum Calculation

Details: Angular momentum is conserved in closed systems, making it fundamental in physics for analyzing rotational motion, orbital mechanics, and quantum mechanics applications.

4. Using the Calculator

Tips: Enter all vector components in Cartesian coordinates. The calculator computes the cross product to determine the angular momentum vector components.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of angular momentum?
A: Angular momentum quantifies how much rotational motion an object has and how difficult it is to stop that rotation.

Q2: How is angular momentum conserved?
A: In the absence of external torques, the total angular momentum of a system remains constant.

Q3: What are the units of angular momentum?
A: kg·m²/s, which combines mass, distance squared, and inverse time dimensions.

Q4: How does angular momentum relate to torque?
A: Torque is the time derivative of angular momentum, similar to how force relates to linear momentum.

Q5: Can angular momentum be negative?
A: Yes, the sign indicates direction relative to the coordinate system's orientation.