B How is tangential velocity measured in m/s when it’s r * w?

[sophiecentaur]

You can use a different ratio.

That is true but, as you know, π will still be a factor in there somewhere. If you re-examine Euler's identity then you will see that π is locked to e and no one mentions radii or diameters.
Good luck with any attempts to design a protractor which will deal conveniently with radian measure.

 

[Orodruin]

I don’t see any issues …….

 

[sophiecentaur]

View attachment 357050

I don’t see any issues …….

That's fine as far as it goes but there are two problems. The scale has fractions, which would make life inconvenient. Also, for rotations (revs) beyond a full turn, your machinist / handyman would have to add multiples of π and that would mean getting familiar with a scale that's not decimal - like everything else we deal with. (I don't include the nonsense of fractional drill and nut sizes, which are just as ridiculous)

PS Draw a dot somewhere on the edge of your image and say, instantly, what the radian value would be. Alternatively imagine a special scale (perhaps decimal) that your average user would take to effortlessly. Not too had to make one with CAD software, I imagine.

Edit. I am an 'old dog' so it may be more difficult for me but a design tech lesson might be hard to deliver even to young dogs.

 

[Orodruin]

The scale has fractions, which would make life inconvenient

So does your regular protractor. Only they are all fractions of 360, which you then multiply by 360.

have to add multiples of

… which is not really any harder than adding multiples of 360.

 

[Ibix]

PS Draw a dot somewhere on the edge of your image and say, instantly, what the radian value would be. Alternatively imagine a special scale (perhaps decimal) that your average user would take to effortlessly. Not too had to make one with CAD software, I imagine.

If you use $\tau$ instead of $\pi$, the scale is effectively just fractions of a complete turn.

 

[Orodruin]

If you use $\tau$ instead of $\pi$, the scale is effectively just fractions of a complete turn.

Shocker!

 

[sophiecentaur]

If you use $\tau$ instead of $\pi$, the scale is effectively just fractions of a complete turn.

That's the literal interpretation of the situation but it's a bnit standing up in a hammock for no reason. Where else in Engineering life do we find that fractions fit in well with our lives. So basically we could divide the circle (or the semicircle) into 100 divisions. Then you could use your calculator. But would anyone be better off than when using 360 degrees? And the factors of 360 make it convenient for mental sums (and making model clocks?)

 

[Orodruin]

That's the literal interpretation of the situation but it's a bnit standing up in a hammock for no reason. Where else in Engineering life do we find that fractions fit in well with our lives. So basically we could divide the circle (or the semicircle) into 100 divisions. Then you could use your calculator. But would anyone be better off than when using 360 degrees? And the factors of 360 make it convenient for mental sums (and making model clocks?)

Again, nothing stops you from dividing the full circle in multiples of $\pi/90$ or $\pi/180$ radians.

 

[sophiecentaur]

That's a great idea. Even I could cope with that one.

 

[A.T.]

The scale has fractions, which would make life inconvenient.

Yes, that's the reason for using 360, which has a lot of integer divisors.

But if one can live with fractions to avoid degree conversions, the sensible choice would be to use the fraction of a full circle (radians as multiples of τ). In fact, that is exactly how children learn to understand fractions:

What never made sense to me is using the fraction of a half the circle (radians as multiples of π).

 

[Orodruin]

When the hits your like a big $\pi$, that’s amore

 

[sophiecentaur]

But if one can live with fractions to avoid degree conversions,

People cannot deal with fractions as easily as you and I can. There is a tale that customers thought that 1/3 pounder burgers were smaller than 1/4 pounder burgers so the competition gave up on that advertising idea

In fact, that is exactly how children learn to understand fractions:

Children may well manage to 'accept the idea' of fractions - or at least say they do. But they use decimals on their calculator as soon as possible. Don't overestimate people just because you find something easy.