Re: imperial screwcutting on metric lathe

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 !

Thank goodness you don't have to understand all that stuff to be able to use
it! :-))

Henry


.

Relevant Pages

  • Re: imperial screwcutting on metric lathe
    ... 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? ... 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. ...
    (uk.rec.models.engineering)
  • Re: imperial screwcutting on metric lathe
    ... Angle in radians x 180 degrees/pi= angle in degrees ... so the angle in Radians and Pi have the same dimension and both are "dimensionless" ...
    (uk.rec.models.engineering)
  • Re: Smarter Scots
    ... radians, ... This allows us to make the small angle approximation, ... To get the sine of that angle, we woulds need to drop an imaginary line ...
    (soc.culture.scottish)
  • Re: Smarter Scots
    ... radians, ... This allows us to make the small angle approximation, ... radius of a circle, then place that piece of string around the ...
    (soc.culture.scottish)
  • Re: Smarter Scots
    ... radians, ... This allows us to make the small angle approximation, ... radius of a circle, then place that piece of string around the ...
    (soc.culture.scottish)