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Yes subject to a condition I can't remember (but one which usually is always satsified for questions).

Sorry for this sh*t answer, the details should be in any good mechanics textbook.

Sorry for this sh*t answer, the details should be in any good mechanics textbook.

Willa

so when considering the instanteous linear motion of a rotating body you DO condense mass down onto the centre of mass?

how does this relate to the previous example - that was a purely rotating system?

If you wish to consider a moving and rotating frame you get evil equations of motion like

a = a' + w' x r' + 2w x r' + 2w x v' + w x (w x r')

But I still don't see how what you're asking relates to the previous problem

RichE

how does this relate to the previous example - that was a purely rotating system?

If you wish to consider a moving and rotating frame you get evil equations of motion like

a = a' + w' x r' + 2w x r' + 2w x v' + w x (w x r')

But I still don't see how what you're asking relates to the previous problem

If you wish to consider a moving and rotating frame you get evil equations of motion like

a = a' + w' x r' + 2w x r' + 2w x v' + w x (w x r')

But I still don't see how what you're asking relates to the previous problem

because the previous problem was exactly the same situation! a rod pivotted about one end falling to the vertical! we concluded you must use 0.5Iw^2 cos it is rotating, but arguably couldnt you say it has 0.5mLw momentum, which means it has p^2/2m = energy = mgL/2. p^2 = m^2gL = (0.5mLw)^2 = m^2L^2w^2/4. So w^2 = 4g/L

that is my problem...using instantenous linear momentum you dont get the right answer!

Willa

that is my problem...using instantenous linear momentum you dont get the right answer!

that is my problem...using instantenous linear momentum you dont get the right answer!

well if you could apply a linear momentum argument like that the whole system potentially could start moving and the pendulum is fixed at a pivot

if everything was moving freely then I think you could apply your argument

but the thing is we applied linear momentum to the impulse stopping the rod rotating...and it works there! why can it work there and not elsewhere! i just dont get it! The linear momentum of the body is definitely mwl/2 if we are to be able to use that in the second question. But then surely you can say that is the instanenous momentum of the whole body...and hence work out it's instanteous energy from that!?

Willa

but the thing is we applied linear momentum to the impulse stopping the rod rotating...and it works there! why can it work there and not elsewhere! i just dont get it! The linear momentum of the body is definitely mwl/2 if we are to be able to use that in the second question. But then surely you can say that is the instanenous momentum of the whole body...and hence work out it's instanteous energy from that!?

well if we applied a greater impulse then consider the difference in what would have happened between a free system and a constrained system

If the system were free at that instant onwards the rod would start moving backwards in the vertical. If constrained such a motion is impossible and I guess the pivot gets jarred and takes some of the momentum.

But this is an educated guess, as I'm arguing on physical grounds and as a (mainly pure) mathematician usually prefer to deal with the numbers.

Does the SR issue make more sense to you now?

RichE

Does the SR issue make more sense to you now?

Does the SR issue make more sense to you now?

unfortunately i have still not resolved that issue to my satisfaction. I devised an unpleasent way of making it work, which involves a way of laying out a length in space as time goes by. But I dont like it as an explanation because it is time dependant. I want to look at the situation from a purely time independant case.

E.g: Stationary observer, S, says "That object is distance x away from me" (this is an object stationary in S frame). S' (moving observer) says "what you on about, it's much closer than that...it's only x' away from me". Hence x = gx'....which i fully understand. And that is what we were taught to be lorentz contraction.

I then imagine another situation, this time something stationary in S' frame. This time the roles are reversed, x' = gx. I fully understand that situation as well.

If you can try and explain how these situations relate to the lorentz transformation then that might help. Because I fail to understand how time comes into these situations

edit: As a guide to the way i think, LM tried to do some maths a few pages back but ended up with x' = gx and tried to claim that x' = x/g from that...which didnt work. If you can fix his working then that would solve my problem, becuase my working (and thinking) is identical to the working he has presented on that page!

LM

we find $l'=x_1'-x_0'$. This gives us:

$\gamma(l-\beta cT)-\gamma(0-\beta cT)=$

$\gamma(l-\beta cT-0+\beta cT)=$

$\gamma l$.

The point here is that you (in frame S) measure the length of a rod at rest, and it measures l. Now it is moving past you at speed v, it will measure $l/\gamma$

$\gamma(l-\beta cT)-\gamma(0-\beta cT)=$

$\gamma(l-\beta cT-0+\beta cT)=$

$\gamma l$.

The point here is that you (in frame S) measure the length of a rod at rest, and it measures l. Now it is moving past you at speed v, it will measure $l/\gamma$

That!

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