Pirouette effect: Calculate Speed and Radius

A simple calculator for the pirouette effect from angular velocity and radius of inertia. The pirouette effect is named after the pirouette in figure skating, a rotation on a point around its own axis. With arms outstretched, the rotation is slower; when the arms are pulled in, the rotation becomes faster. Angular velocity is the number of revolutions per time. Radius of inertia is the point where a point-shaped mass would have the same moment of inertia, it is greater than 0 and less than the total radius and can often only be estimated.

Angular velocity ω₁:		rp
Radius of inertia i₁:
Angular velocity ω₂:		rp
Radius of inertia i₂:

Please enter three values for angular velocity and radius of inertia, the fourth value will be calculated. The unit of length for the radius is arbitrary, but the same for both radii.

The formula for the calculation is: ω₁ * i₁² = ω₂ * i₂²

Example 1: a figure skater performs a pirouette. With outstretched arms, her radius of gyration is 48 centimeters, she makes one rotation per second. If she pulls the arms and reduces the radius to 20 centimeters, then the rotation speed increases to 5.8 revolutions per second.

Example 2: an interstellar gas cloud has a radius of inertia of 20 astronomical units and rotates once every 100 years (0.01 rev/year). The resulting star has a radius of inertia of 0.003 astronomical units (448793 km). If it had retained all the angular momentum by itself, its spin rate would be 50.7 revolutions per hour - far too fast for a star, it would tear apart. Therefore, multiple stars or planetary systems are formed from the gas cloud, in which the angular momentum is mainly in the rotation around each other.

Physics commonly uses SI units. Here is a calculator to convert units.