# Length contraction problem of right angled triangle

1. Mar 3, 2013

### djsourabh

http://https://www.physicsforums.com/attachment.php?attachmentid=56297&stc=1&d=1362318192 [Broken]problem:-
The situation is shown in attachment.
the right angled frame of rods (in stationary ) is moving at speed v perpendicular to its hypotenuse.
according to length contraction the corresponding lengths of sides should contract.
So it may not remain a right angled triangle in moving frame.
but if 'V' is such that L*cos(90-a) contracts such that L contracts than half of hypotenuse (h/2) .
we know that hypotenuse can not contract .
Also both L(AB) & L(AC) contract less than h/2. what happens in that case?
(L is the length of each side, consider isosceles triangle.
∠a is the angle opposite to point A)

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2. Mar 3, 2013

### Staff: Mentor

The attachment is missing.

3. Mar 3, 2013

### djsourabh

i am trying to figure out why.

4. Mar 3, 2013

### Staff: Mentor

OK, in the meantime I will answer from what I can understand by your verbal description as much as possible. From your description it sounds like the hypotenuse is perpendicular to the direction of motion and the "legs" are each oblique to the direction of motion. For an oblique angle you can separate that into a parallel and perpendicular component. The perpendicular component will not length contract at all, only the parallel component. So no matter how great the length contraction you will always have a triangle (though not a right triangle).

5. Mar 3, 2013

### djsourabh

thank you i got what you are trying to tell.
but i am not getting the reason why the lengths of sides should tilt towards hypotenuse as if they are going to coincide hypotenuse.why their position or angle should change?
and how?

6. Mar 3, 2013

### Staff: Mentor

Imagine, instead of a triangle, you have a series of rods of different lengths all stacked closely together. Each rod is oriented parallel to the direction of travel (perpendicular to the hypotenuse), the front ends are lined up with the hypotenuse, and the length of each rod is such that the back end lands on one of the legs of the triangle. So the outline of the stack of rods coincides with the triangle.

Now, each rod is going parallel to the direction of travel, so each one is contracted according to the standard length contraction formula. What is the resulting outline shape?

7. Mar 3, 2013

### djsourabh

yes sir ,resulting locus is the sides of triangle.