Re: imperial screwcutting on metric lathe

Mark Rand wrote:
On Tue, 23 Dec 2008 20:50:43 +0000, Cliff Ray <cliffrayS@xxxxxxxxxxxxxxxxxxxx>
wrote:


What unit does pi have then?

If pi x angle in radians = angle in degrees, don't both sides of the equation need to have the same units, which would mean pi and angle in radians can't both be unit-less?

Neither degree or radian has dimension, unless it's "angle" - which is not usually considered to be a dimension.

The natural pseudo-dimensional unit of angle is "rotation-through-360-degrees", but it doesn't behave like conventional dimensional units, eg firkins or MM pork pies - take a point, add a length dimension unit to it and it stretches into a line - but add a rotation dimension unit, and the point is unchanged.

Do it twice, rotate through 720 degrees, and you still end up in the situation where you started. Same if you square it, conventionally interpreted geometrically as rotating it through a plane orthogonal to the plane of the first rotation - the object is unchanged.

Rotations are something - but as they don't behave like dimensions, they can't be a dimension.

Usually they are simply ignored in dimensional analysis.


Oddly enough there is a far better explanation on wikipedia than I can give.
Suffice it to say that in mathematics and the mathematical end of engineering,
angles are radians and logs are to base E for very sound reasons. And yes,
radians are specifically dimensionless as are revolutions! (I well remember
the bollocking for quoting a speed in rpm instead of m^-1 :-( )

I'm confused - rpm is a rotation rate, and has dimension 1/time and units 1/s - speed has dimension length/time, and units m/s.



It all makes sense to those that can still remember how to do calculus, as
opposed to us old farts vaguely repeating what was beaten into us.


Mark Rand
RTFM

-- Peter Fairbrother

(an old fart who's forgotten most of the calculus once literally beaten into him, but who does advanced math, number theory, group theory and so on (almost) every day)

ps Hi Nick nice to see you back :)

pps Merry Xmas all !
.

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