# Derived dimensions

*DimensionfulAngles.jl* also defines derived dimensions that include angle. These are:

`DimensionfulAngles.SolidAngle`

`DimensionfulAngles.AngularVelocity`

`DimensionfulAngles.AngularAcceleration`

.

This allows, among other things, dispatching on these derived dimensions.

Several units are defined for these derived dimensions, including the steradian for solid angle and RPM for angular velocity.

*DimensionfulAngles.jl* also provides `Periodic`

a UnitfulEquivalences.jl `Equivalence`

to convert between period, frequency, and angular frequency of a periodic response.

## Solid Angle

Solid angle is a two-dimensional angle subtended at a point. In the SI system it has units of $m²/m²=1$ and is non-dimensional. Here, following several proposed systems, it has dimensions of angle squared, `𝐀²`

. See Relation to proposed SI extensions. The SI unit of solid angle is the steradian, which here is defined as $sr=rad²$. The steradian takes SI prefixes and therefore defines many other units (e.g., the millisteradian `DimensionfulAngles.msrᵃ`

). These are documented in Prefixed units.

Missing docstring for `DimensionfulAngles.SolidAngle`

. Check Documenter's build log for details.

Missing docstring for `DimensionfulAngles.srᵃ`

. Check Documenter's build log for details.

## Angular velocity and acceleration

Content:

Angular velocity has dimensions of angle over time `𝐀/𝐓`

and can be used to measure different quantities such as rotational velocity, rotational speed, and angular frequency of a phase angle. Two units of angular velocity are defined: the revolutions per second (RPS) and the revolutions per minute (RPM), provided as `DimensionfulAngles.rpsᵃ`

and `DimensionfulAngles.rpmᵃ`

respectively.

Angular acceleration is the time rate of change of angular velocity and has dimensions of angle over time squared `𝐀/𝐓²`

. No units are defined specifically for this derived dimension.

Missing docstring for `DimensionfulAngles.AngularVelocity`

. Check Documenter's build log for details.

Missing docstring for `DimensionfulAngles.AngularAcceleration`

. Check Documenter's build log for details.

Missing docstring for `DimensionfulAngles.rpsᵃ`

. Check Documenter's build log for details.

Missing docstring for `DimensionfulAngles.rpmᵃ`

. Check Documenter's build log for details.

### Periodic equivalence

For periodic responses there are several analogous ways to measure the repeat period: period `T`

(`𝐓`

, `s`

), frequency `f`

(`1/𝐓`

, `Hz=1/s`

), or angular frequency `ω`

(`𝐀/𝐓`

, `rad/s`

). These are related by

$f = 1/T = ω/2π$.

*DimensionfulAngles.jl* provides `Periodic`

a UnitfulEquivalences.jl `Equivalence`

to convert between period, frequency, and angular frequency of a periodic response.

Missing docstring for `DimensionfulAngles.Periodic`

. Check Documenter's build log for details.

## Syntax

Contents:

### Syntax provided by *Unitful.jl*

Missing docstring for `DimensionfulAngles.AngularVelocityUnits`

. Check Documenter's build log for details.

Missing docstring for `DimensionfulAngles.AngularVelocityFreeUnits`

. Check Documenter's build log for details.

Missing docstring for `DimensionfulAngles.AngularAccelerationUnits`

. Check Documenter's build log for details.

Missing docstring for `DimensionfulAngles.AngularAccelerationFreeUnits`

. Check Documenter's build log for details.

Missing docstring for `DimensionfulAngles.SolidAngleUnits`

. Check Documenter's build log for details.

Missing docstring for `DimensionfulAngles.SolidAngleFreeUnits`

. Check Documenter's build log for details.

### Prefixed Units

```
Modules = [DimensionfulAngles]
Filter = x->_filter_prefixed("sr", x)
```