3 ms·
This has always bothered me, that there were dimensionless units that a dimension-like quality, like radians.
by QuesnayJr 6y ago
This has always bothered me, that there were dimensionless units that a dimension-like quality, like radians.
- thaumasiotes 6y agoSeriously, radians aren't dimensionless. If you calculate arclengths using angles measured in degrees, the whole problem disappears: a 60° arc around a circle of radius 3cm has length equal to (2·pi·3cm·60°)/(360°) = (2·pi·3cm)/6 = pi centimeters. Looking at it that way makes it very plain that the angles have units attached, and those units don't appear in the result of "pi centimeters" because they canceled out during the computation. This is overt when calculating in degrees because they are an inconvenient size. The size of a radian is chosen so that the constant terms (2·pi) in the numerator and (2·pi radians) in the denominator appear to cancel out, giving a (1 radian) in the denominator which is omitted from the formula because dividing by 1 is numerically pointless. But dividing by 1 radian is not dimensionally pointless; omitting the 1 from the formula leads to the illusion that θ has no unit attached.