A simple contraction question.

[MathematicalPhysicist]

A rod. having slope m relative to the x-axis of S, moves in the x direction at speed u. what is the rod's slope in the usual second frame S'? (S is at rest realtive to S' which moves along the x direction with velocity v).
well obviously the horizontal length of the rod is contracted or lengthened, depends on your frame:
i think that if L is the length of the rod, and $$u'=\frac{u-v}{1-\frac{uv}{c^2}}$$ then we have: L'_x=Lcos(theta)/gamma(u')
and the slope in S' is: m'=m*gamma(u') cause the vertical portion of the rod doesn't get change.

the problem is that in the answer key we have:
m'=m*gamma(v)*(1-uv/c^2)
but i don't get this, even with some algebraic manipulations, so i guess I am wrong here, can someone help here?

thanks in advance.

 

[neutrino]

S is at rest realtive to S' which moves along the x direction with velocity v

 

[MathematicalPhysicist]

S is at rest relative to S', where S' moves with horizontal velcoity compared to S, what's not understood here?

 

[Doc Al]

S is at rest relative to S', where S' moves with horizontal velcoity compared to S, what's not understood here?

(1) S is at rest relative to S'
(2) S' moves with a horizontal velocity compared to S

Sounds contradictory to me! You might want to reword your problem statement.

 

[MathematicalPhysicist]

what's wrong here?
one frame is stationary the other one moves with constant speed, what's wrong with this?

 

[neutrino]

In SR, you cannot say that something is at rest in an absolute sense. It has to at rest with respect to/relative to something. So if S' is at rest with respect to S, then the relative velocity between the two is 0. If, on the other hand, S' has a velocity of v as measured by S, then S' measures the velocity of S to be -v(assuming standard configuration).

 

[MathematicalPhysicist]

yes i see your point, i meant that S' has velocity v as measured by S.

 

[neutrino]

yes i see your point, i meant that S' has velocity v as measured by S.

Now that we have taken care of that, back to the problem...

I don't really see how to manipulate your answer, which is correct, to the form given in the book, and I also don't see how it is simpler than just having gamma(u').