# Speed of Circular Motion

vCalc Reviewed
v =
Speed of Circular Motion
Variable Instructions Datatype
(T) "Period" Enter the time it takes to complete one full cycle Decimal (s)
(r) "Radius" Enter the radius of the circular motion Decimal (m)
Rating
ID
vCalc.Speed of Circular Motion
UUID
af6582a4-8fc4-11e4-a9fb-bc764e2038f2

The Speed of Circular Motion calculator computes the speed (s) of a particle or point in uniform circular motion based on the radius (r) of the orbit and the period of rotation, T.
INSTRUCTIONS: Choose your preferred units (e.g. nano-meters or milliseconds) and enter the following:

• r This is the radius defining the orbit of circular motion.
• T This the orbital period of rotation.

The calculator computes the Speed of Circular Motion (v) in meters per second.  However this can be automatically converted to numerous other velocity units via the pull-down menu.

Exercise: Choose Years as the units for period, and Astronomical Units as the unit for radius.  Then enter 1 as the value for both.  The resulting velocity is the speed that the Earth travels about the Sun.  Then use the pull-down menu to see the result in miles per hour (mph).

### 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.

The distance around the circular path is  d = 2*pi*r (2*pi radians is one complete rotation) and then  v = d / T is the velocity.

So, v = (2*pi*r) / T

## Other Circular Motion Functions

• Centripetal Acceleration as a function of tangential velocity and radius, CLICK HERE.
• Angular Frequency as a function of orbital period, CLICK HERE.