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raf

06:09

In Goldstein, the infinitesimal rotation formula gives: $$d\mathbf\Omega = \mathbf{n} d \Phi$$
here, $d\mathbf\Omega$ is the differential vector!
What does $\mathbf\Omega$ mean? What should it be called?

ACuriousMind

07:02

@Phase as far as I understand it, a squiggly line just means "this can point either up or down"

ACuriousMind

07:31

@raf it's the rotation vector or Euler vector

raf

@ACuriousMind but in the footnote, it's said that: It can not be emphasized too strongly that $\mathbf\Omega$ is not the differential of a vector. ... there is no vector of which $\mathbf\Omega$ represents a differential.

I am confused with these idea.

ACuriousMind

I think what Goldstein means by that is that there "is" no actual quantity that corresponds to this - it is a purely mathematical representations of a rotation, it's not a physical quantity like "velocity"

raf

07:46

sorry for typo.
It's said that: "It can not be emphasized too strongly that $d\mathbf \Omega$ is not the differential of a vector. ... there is no vector of which $d\mathbf \Omega$ represents a differential."

user129412

Do I exert 1 atm of pressure on the atmosphere?

John Rennie

08:08

@user129412 yes, that's why if we suddenly put you in a vacuum you would expand (with unpleasant consequences :-)

user129412

I'm not sure I've heard of that before. I think you would swell from decompression, and maybe your lungs would rupture, but you would also expand?

Or is the swelling from decompression what you meant?

John Rennie

I think the only bit of you that would swell much is the air in your lungs, and as long as you kept your mouth open you'd be OK as the air would just escape.

I don't know if we've ever done the experiment of exposing humans to a vacuum, but divers ascending from depth can suffer burst lungs due to the rapid pressure drop.

user129412

08:25

There is also some air in your other organs, but maybe the tissues are firm enough to hold that back

John Rennie

We could try the experiment, but finding a volunteer could be hard :-)

user129412

Indeed. I'm surprised they haven't tried with animals, in less ethical endeavours. The doesn't seem to be much info on it. But that's probably for the best (for the chimps)

Oh, apparently NASA did in 1965. Not outer space, but still 0.031 psi for 30 seconds. They were fine afterwards

And apparently Tardigrades do not care about either the vacuum or the radiation

Anyway, this is leaving the realm of physics, I suppose!

5 hours later…

Ali

14:01

Umm, Is this an appropriate place to ask a high school physics question here ? And if yes, how do I send a picture here ?

Ali

14:28

ibb.co/qkSqwRR

Here is the question. I don't need a solution for it. I already have it. I just wanted to know how will even the block and the pulley move without making the strings loose since all the strings are tight and one end is attached to a wall.

Another problem I had was regarding the acceleration of the pulley. The pulley is massless. So, It should have infinite acceleration for even a small amount of force. But it doesn't! The solution I have ,calculates the acceleration of the massless pulley by some other clever way.

Also, is there a world limit for the messages I send here ?

ACuriousMind

@Ali We have a dedicated room for high school physics

You can upload images by clicking on the "upload" button to the right of the text field, but you may need to switch to the desktop site to see it