The Angular Frequency calculator computes an angular frequency (?) based on an input period of rotation, T.

INSTRUCTIONS:  Choose the preferred units and enter the following:

• T: This is the period of rotation.

Angular Frequency(?): The calculator computes the Angular Frequency (?) in radians per second.  However, this can be automatically converted to other angular frequency units (e.g. degrees per minute) via the pull-down menu.

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• Astronomy Calculator

The Math

The angular frequency is the number of increments of `2*pi` radians (`2*pi` radians is one complete rotation) divided by the period of the rotation, outputting simply rotations per unit time.

Since frequency is the inverse of period, `f = 1/T` ^[1], and angular frequency is a multiple of frequency: `omega = 2*pi*f`, we can substitute for frequency, f and get the angular frequency as a function of period:

`omega = (2*pi) /T`

Other Circular Motion Functions

• Centripetal Acceleration as a function of tangential velocity and radius, CLICK HERE.
• Speed of Circular Motion as a function of orbital period and radius, CLICK HERE.
• Radial Acceleration as a function of orbital period and radius, CLICK HERE.
• Acceleration in non-uniform Circular Motion, CLICK HERE.

Sources

Young, Hugh and Freeman, Roger.  University Physics With Modern Physics.  Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 421, eq 13.2

1. ^ Young, Hugh and Freeman, Roger.  University Physics With Modern Physics.  Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 420, eq 13.1