Speed of Circular Motion

vCalc Reviewed
Equation / Last modified by AndrewBudd on 2019/08/15 19:52
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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 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.
  • Radial Acceleration as a function of orbital period and radius, CLICK HERE.
  • Acceleration in non-uniform Circular Motion, CLICK HERE.
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References

  1. ^ Young, Hugh and Freeman, Roger.  University Physics With Modern Physics.  Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 89, eq 3.29