Degrees of freedom

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Degrees of freedom

A degree of freedom is a number that specifies some information about a system and which is not fixed a priori. For example, an infinitely small ball rolling down a track has only one degree of freedom: its position in the track. However, if we substitute the track for a plane, the ball will have two degrees of freedom. If we allowed the ball to have a size, it would also be able to rotate on itself: thus, it would have an additional degree of freedom for every angle, since they also would not be fixed.

Degrees of freedom are sometimes referred to as “dimensions”, though the latter are normally used for space and the former are used more loosely, for any system with undetermined parameters (for example, in a thermodynamical system).

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