# Length Contraction from an Angle

• SpaceTrekkie
In summary, the length of a meter stick, moving with 0.8C relative to frame S, when measured by an observer in S and at a 60 degree angle to the direction of motion, is 0.917 meters. This can be solved by considering the meter stick as the hypotenuse of a 30-60-90 triangle in both the original and moving frames, and using the fact that length contraction only occurs in the direction of motion.
SpaceTrekkie

## Homework Statement

A meter stick is moving with 0.8C relative to frame S. What is the sticks length when measured by an observer in S if the stick is 60 degrees to v, as seen in the rest frame?

## Homework Equations

Length contraction = proper length /lorentz factor

## The Attempt at a Solution

Okay for the speed I got the lorentz factor = 1.66667. So if the meter stick was moving directly parallel the length would be contracted to .6 meters. I know that length contraction only occurs in the direction of motion, so NOT perpendicular. And I know that I can solve it by thinking about the meter stick as the hypotenuse of a 30-60-90 triangle. I think I am just mis visualizing something, but I really can't seem to work it out. I looked in the back of the book and the answer is .917 meters. I used that to try to work backwards and still could not figure it out.

Any direction would be awesome...

Hi SpaceTrekkie!
SpaceTrekkie said:
Okay for the speed I got the lorentz factor = 1.66667.
So if the meter stick was moving directly parallel the length would be contracted to .6 meters. I know that length contraction only occurs in the direction of motion, so NOT perpendicular.
And I know that I can solve it by thinking about the meter stick as the hypotenuse of a 30-60-90 triangle.

All correct.

Draw the triangle in x,y coordinates.

Now draw it again in x',y' coordinates.

y' = y and x' = 0.6x, so … ?

Hmm, Does it work to change the x and y-axis so that they x-axis is in like with the direction of motion? I think that might make it easier, or am I over thinking the problem?

SpaceTrekkie said:
Hmm, Does it work to change the x and y-axis so that they x-axis is in like with the direction of motion? I think that might make it easier, or am I over thinking the problem?

No, you're completely correct

always have one of the axes in the direction of motion …

otherwise the equations get too complicated!

## 1. What is length contraction from an angle?

Length contraction from an angle is a concept in special relativity where the length of an object appears to be shorter when observed from an angle, as opposed to being observed directly from the front or back.

## 2. How does length contraction from an angle occur?

Length contraction from an angle occurs due to the effects of the Lorentz transformation, which describes how space and time are perceived differently by observers in different reference frames moving at different velocities.

## 3. Is length contraction from an angle a real phenomenon?

Yes, length contraction from an angle is a real phenomenon that has been observed and confirmed through experiments and theoretical calculations. It is a consequence of the principles of special relativity.

## 4. Does length contraction from an angle only occur at high speeds?

No, length contraction from an angle can occur at any speed, but it becomes more noticeable at high speeds approaching the speed of light. At lower speeds, the effect is too small to be observed.

## 5. What are some practical applications of length contraction from an angle?

Length contraction from an angle is a fundamental concept in special relativity and is important in understanding phenomena such as time dilation and the twin paradox. It also has practical applications in fields such as particle physics, where high-speed particles are studied and their lengths appear shorter due to length contraction.

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