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# Pirouette effect: Calculate Speed and Radius

The formula for the calculation is: _{1} * _{1}² = _{2} * _{2}²

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.