## Angular Units

Simscape™ implementation of angular units relies on the concept of angular units, specifically radians, being a unit but dimensionless. The notion of angular units being dimensionless is widely held in the metrology community. The fundamental angular unit, radian, is defined in the Simscape unit registry as:

`pm_addunit('rad', 1, 'm/m');`

which corresponds to the SI and NIST definition . In other words, Simscape unit manager does not introduce a separate dimension, `'angle'`, with a fundamental unit of `'rad'` (similar to dimensions for length or mass), but rather defines the fundamental angular unit in terms of meter over meter or, in effect, `1`.

The additional angular units, degree and revolution, are defined respectively as:

```pm_addunit('deg', pi/180, 'rad'); pm_addunit('rev', 2*pi, 'rad');```

As a result, forward trigonometric functions, such as `sin`, `cos`, and `tan`, work directly with arguments expressed in angular units. For example, cosine of 90 degrees equals the cosine of (pi/2) radians and equals the cosine of (pi/2). Expansion of forward trigonometric functions works in a similar manner.

Another effect of dimensionless implementation of angular units is the convenience of the work-energy conversion. For example, torque (in N*m) multiplied by angle (in rad) can be added directly to energy (in J, or N*m). If you specify other commensurate units for the components of this equation, Simscape unit manager performs the necessary unit conversion operations and the result is the same.

### References

 The NIST Reference on Constants, Units, and Uncertainty, `https://physics.nist.gov/cuu/Units/units.html`