imperial screwcutting on metric lathe

On or around Tue, 23 Dec 2008 19:53:51 +0000, Cliff Ray enlightened us thusly:

it is, but one radian is about 57.summat degrees, since the 3rd side is curved, not straight.

the thing about dimensions is right though.

But it doesn't!

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"

Bob

It doesn't!

It doesn't!

You are suggesting that 1 Radian is 3.145926° when in fact it is

The angle in degrees is in fact equal to the angle in Radians DIVIDED by Pi and then multiplied by 180 (360° = 2 Pi Radians) ----- R/pi*180°

So the unit (degrees) is determined by the unit of the final multiplicand (180°) since all other variables are unitless.

JG

Your post came down as I was sending mine, Bob.

We are both saying the same thing of course, just choosing to write the equation differently.

JG

So miles per gallon being length per length cubed should be per square metre?

lbs and oz if the Melton Mowbray versions

Last time I bought one I didn't buy it by weight; I simply bought

Regards, Tony

Okay.

2)I give in.

Well as they say two out of three aint bad, so maybe one of those could be a lie :)

Quite so, allowing for the fact that neither miles nor gallons are in m^3, but the principle is correct. The 'error' as such would be a simple ratio (dim-less number) of miles/m per gallons/m^3. It can be useful in checking that you've got relationships in equartions correct. As noted earlier, both sides of an equals sign must have the same dimensions.

When working with any of the heap of dimensionless numbers (eg Reynolds, Mach, Froude, Nusselt etc etc) or some of the more obscure units (viscoscity gives some of the most strange, being pressure-seconds) totting up the string of dimensions and checking that they do cancel to the desired result is a quick easy means to see if you've made a basic clanger. More subtle clangers are still entirely possible;-)

Richard

In article , Amateur machinist writes

That would be dimensionally correct. Of course, you could equally well quote sfc in litres per kilometre (hence having dimensions L^2) or kilograms per kilometre (ML^-1) or even joules per kilometre (MLT^-2). Such conversion factors necessarily take their dimensions from the units chosen for their definition; any attempt to relate them to other meaningful parameters will likely drive you nuts. Richard's recent post is entirely in point here.

David

There are some unobscure derived quantitiess which when expressed in SI base units can look incromprehensible. Try these two.

1. m^2 kg s^-3 A^-2
2. m^-2 kg^-1 s^4 A^2

Well I can read a screwcutting chart but I can't understand that.............

John S.

Resistance and capacitance, at least I am good at electricity :)

If you purchased one, but then wanted to verify that the weight was as described on the packaging, where would you for an accurate measurement that would stand up in a court of law?

Well, in the words of the old song ...

"Somewhere, over the rainbow, weigh a pie"

Yes, it resolves to 1/length^2, and so can be expressed in reciprocal acres or reciprocal ares. Alternatively, following the convention established for conductivity, in ercas or eras.

Regards,

David P.

I hope you are aware of the old, but emerging contender to replace the ISO (MKS) system towit the FFF system ie Furlong, Firkin, Fortnight. With a distance, a mass and a time, ALL other units can be derived. Gives rise to some delightful but concise units eg the earlier mpg becomes furlongs/firkin, - I doubt I could manage the reciprocal firkin/furlong, but I'd be willing to try as long as it was Speckled Hen or HSB

Richard

Indeed, from my university days in the early 1960s. A reasonable proposition in a time of great change. O levels used crs for physics, ft lbm s for math, then all change for A level, kg m s and ft slug s respectively, ie all four combinations of Imperial and metric, gravitational and absolute in 2 years. If the buggers were going to take the piss, we wanted our fun, too.

I recall the firkin per fortnight, - being the average bitter consumption of a young, virile, rugby playing but impecunious ee student.

I'll probably manage that over Christmas with a combination of OSH at home / parties, and draught Marston's Peedegree at the pub. These days, it doesn't take many pints for me to reach the equilibrium state, ie one pint out for every pint in. :-((

Regards,

David P.

Could you expund on what is your own practical application of Group Theory, and how you actually do meaningful calculations with it?

Whenever I've come across Group theory in school textbooks my reaction is always, "How curious!" because I cannot see any practical application for it.

In article , Amateur machinist writes

Symmetry point groups are very important in chemistry, crystallography, and (I imagine) metallurgy.

My wife (a mathematician) tells me that this is not "real" group theory, by which I think she means it is a fairly obscure (to mathematicians) special area of group theory which happened to lie outside university maths courses.

David