## Units for Angular Velocity and Frequency

Angular velocity units, such as
`rad/s`

,
`deg/s`

, and
`rpm`

, can also be used to
measure frequency for cyclical processes. This is
consistent with frequency defined as revolutions
per second in a mechanical context, or cycles per
second in an electrical context, and lets you
write frequency-dependent equations without
requiring the `2*pi`

conversion
factor. In the SI unit system, however, the unit
of frequency is hertz (Hz), defined as
`1/s`

.

Simscape™ software defines the unit hertz
(`Hz`

) as `1/s`

,
in compliance with the SI unit system. This
definition works well when frequency refers to a
nonrotational periodic signal such as the
frequency of a PWM source. For cyclical processes,
however, the block equations have to contain the
`2*pi`

conversion factor, to
convert the numerical value specified in
`Hz`

, or
`s`

^{-1},
to angular frequency.

As a result, frequency units (based on
`Hz`

) and angular velocity units
(based on `rpm`

) are not directly
convertible, and using one instead of the other
may result in unexpected conversion factors
applied to the numerical values by the block
equations. For example, the AC Voltage
Source block explicitly multiplies the
value you specify for its
**Frequency** parameter by
`2*pi`

, to convert it to angular
frequency before calculating the sine
function.

Drop-down lists of suggested units in block
dialogs and Property Inspector reflect this distinction. For example, if a block has a
**Frequency** parameter with the default unit of `Hz`

, the
drop-down list for this parameter contains only units directly convertible to Hz (such as
`kHz`

, `MHz`

, and `GHz`

) and does not
contain the angular velocity units. Conversely, if you define a custom block where the
**Frequency** parameter has the default unit of `rpm`

, its
drop-down list of suggested units will include `deg/s`

and
`rad/s`

, but will not contain Hz, `kHz`

,
`MHz`

, or `GHz`

.

When you type a unit expression in the
parameter units combo box (instead of selecting a
value from the drop-down list), the Simscape unit manager considers the units of
frequency and angular velocity to be commensurate.
For example, when the default parameter unit is
`Hz`

, you are able to type not
only `1/s`

, but also expressions
such as `deg/s`

and
`rad/s`

. This behavior is
consistent with the Simscape implementation of angular units (see
Angular Units). It
is your responsibility to verify that the unit
expression you typed works correctly with the
block equations and reflects your design
intent.