# Speed of Circular Motion

vCalc Reviewed
Equation / Last modified by AndrewBudd on 2019/08/15 19:52
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vCalc.Speed of Circular Motion
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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 units and enter the following:

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

Speed of Circular Motion (v): The calculator computes the velocity 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

#### Astronomy Calculators

• Kepler's 3rd Law formula T² = (4π • R³)/(G • M)
• Small Angle Formula
• Flux and Magnitude formulas
• Telescope formulas
• Mass formulas
• Relative Size Formulas
• Wavelength Formulas
• Luminosity and other Formulas
• Centripetal Acceleration as a function of tangential velocity and radius, CLICK HERE.
• Angular Frequency as a function of orbital period, CLICK HERE.