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What's the difference between revolutions and radians?

1 Answer

Jul 5, 2015

A factor of $2 π$ $2pi$ .

One revolution traces out $2 π$ $2pi$ radians.

Explanation:

The circumference of a circle of radius $r$ $r$ has length $2 π r$ $2pi r$

A radian is the angle subtended by an arc of length equal to the radius. That is, if the radius is $r$ $r$ , then the length of the arc is $r$ $r$ .

For an arc to subtend a full revolution its length must be $2 π r$ $2pi r$ so the angle is $2 π$ $2pi$ radians.

I hope that helps!

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