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.