Does the ratio of the mechanical degrees of a generator to 360 degrees have a specific term and symbol?
If \$\theta_m\$ is given in degrees, then \$\frac{\theta_m}{360}\$ is the angle given in (fractional) &quot;turns&quot;.
If \$\theta_m\$ is given in radians, then \$\frac{\theta_m}{2\pi}\$ would be the angle given in (fractional) turns.
In either case, the \$360\$ or \$2\pi\$ is simply a factor to convert from degrees (or radians) to (fractional) turns.
However, note that the (fractional) &quot;turns&quot; in this case, is simply a way to  describe an angle, not the number of electrical winding turns.
https://en.wikipedia.org/wiki/Turn_(angle)