Math CentralQuandaries & Queries


Question from Brian, a teacher:

I'm teaching Precalculus right now and will be covering the formula to convert angular speed into linear speed. My question is about the units involved. Using v=rw, if r is mearsured in feet and w is measured in radians/second then v is measured in ft/sec. What happened to the units of radians? I can't find a good way to explain why they are not part of units for velocity. Do you have a good explanation?

Hi Brian.

Radians are not true units, just as percentages aren't true units. A radian is simply an angle or a part of a circle. We have ten fingers and ten toes (usually) so we like base 10. That makes percentages (fractions out of 100) particularly convenient.

With cycles (circles, periods, revolutions, angular measurements), we find it easiest to work not in 100ths of a whole but in "2 pi-ths" of a whole. So they are really just a particular kind of fraction.

Stephen La Rocque.

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