SR length contraction question

In summary, the length of a rod moving along the x-axis with speed u relative to inertial frame S would be contracted to L' when measured from a different inertial frame S' moving with speed v. The formula for length contraction, L=L' * sqrt(1-square(v/c)), can be used by substituting the speed of the rod relative to S' instead of v. This speed can be calculated as (u+v)/(1+uv/c^2).
  • #1
ehasan
9
0
A rod moves along x-axis with speed u and has length L relative to Inertial Frame S. What is its length L' relative to the other inertial S' that moves with speed v with respect to S.

I know the famous length contraction formula L=L' * sqrt(1-square(v/c))
but I confuse how to include velocity of the rod (u) in this formula...:confused:
thanks
 
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  • #2
The speed of the rod relative to inertial system S' would be [itex](u+ v)/(1+ uv/c^2)[/math]. Put that into the contraction formula rather than v.
 
  • #3
HallsofIvy said:
The speed of the rod relative to inertial system S' would be [itex](u+ v)/(1+ uv/c^2)[/math]. Put that into the contraction formula rather than v.

Thanks a lot for making it clear to me
 

What is SR length contraction?

SR length contraction, also known as Lorentz contraction, is a phenomenon in special relativity where the length of an object appears shorter when measured in the direction of its motion relative to an observer.

What causes SR length contraction?

The cause of SR length contraction is the concept of time dilation, where time appears to pass slower for objects moving at high speeds. This, combined with the idea of the constancy of the speed of light, leads to the phenomenon of length contraction.

How does SR length contraction affect measurements?

SR length contraction affects measurements by making objects appear shorter when measured in the direction of their motion. This is due to the fact that time appears to pass slower for objects in motion, causing their length to appear shorter to an observer at rest.

Is SR length contraction observable?

Yes, SR length contraction has been observed and confirmed through various experiments, such as the famous Michelson-Morley experiment. It has also been observed in high-speed particle accelerators, where the particles appear to contract in the direction of their motion.

Does SR length contraction only occur in one direction?

No, SR length contraction occurs in the direction of an object's motion relative to an observer. This means that if an object is moving in multiple directions, it will appear shorter in all of those directions when measured by an observer at rest.

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