Angular Momentum⚠ unverified
Physics / Mechanics · Compute angular momentum of a point mass about an axis
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| mass | mass | kg | 1.0 | Mass of the body |
| velocity | velocity | m/s | 1.0 | Speed of the body perpendicular to the radius |
| radius | radius | m | 1.0 | Perpendicular distance from the axis of rotation |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | L | kg*m^2/s | Angular momentum, in kilogram-metres squared per second (kg*m^2/s) |
The science & history
Understanding the Parameters
- $m$, $v$ — linear momentum magnitude is $p = mv$; angular momentum scales with both.
- $r$ — lever arm from the origin to the particle. Choice of origin matters.
- $L$ — measures “amount of rotation” about that origin; conserved when net external torque is zero.
Derivation (Approaching a Proof)
By definition $\mathbf{L} = \mathbf{r}\times\mathbf{p} = \mathbf{r}\times(m\mathbf{v})$. Magnitude: $L = m v r\sin\phi$. For motion in a circle of radius $r$ with speed $v$ (or any instant with $\mathbf{v}\perp\mathbf{r}$), $\sin\phi = 1$ and $L = mvr$. For a rigid body about a fixed axis, $L = I\omega$ (see Moment Of Inertia Point Mass, Torque).
History
Angular momentum conservation (Kepler’s second law as areal velocity, then general mechanics) is a cornerstone of orbital dynamics and quantum physics; the classical $mvr$ form is the introductory case.
Related Concepts: Momentum, Torque, Centripetal Force, Moment Of Inertia Point Mass, Circular Orbital Velocity
Notes: Registry calculator angular-momentum (unverified). Perpendicular special case only; not
$I\omega$ for extended bodies unless $I = mr^{2}$ and $v = \omega r$.