Radians:

The other technique of specifying fractions of an ac cycle is to divide it into accurately 2π, or around 6.2832, equivalent parts. This is the number of radii of a circle which can be laid end to end about the circumference. One radian, is represented by rad (though you can write out the entire word), is equivalent to around 57.296°. Physicists use the radian more frequently than the degree whenever talking about fractional parts of an ac cycle.

At times the frequency of an ac wave is measured in radians per second (rad/s) instead of in hertz (cycles per second). Since there are 2π radians in a complete cycle of 360°, the angular frequency of a wave, in radians per second, is equivalent to 2π times the frequency in hertz. Angular frequency is represented by the lowercase italicized Greek letter omega (ω).

PROBLEM:

Determine the angular frequency of household ac? Suppose that the frequency of utility ac is 60.0 Hz.

SOLUTION:

Multiply the frequency in hertz by 2π. When this value is taken as 6.2832, then the angular frequency is

ω = 6.2832 x 60.0 = 376.992 rad/s

This mustbe rounded off to 377 rad/s since our input data are given only to three significant figures.