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# 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) |

vCalc.Speed of Circular Motion

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**. - 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

- ^ 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

**Speed of Circular Motion**, references 1 equation/constant.

**Equations and Constants **

**Speed of Circular Motion**, is used in 4 calculators.