# Relativity 2

## Example 2: Length Contraction

**The Question:**  Length contraction is a more difficult thing to wrap your head around and practical example of it are harder to conjure up. You'll read about one in the text. 

Let's run with a ruler (not scissors). 

***The scenario:***

* Meter stick is own rest frame (the "proper frame") and of course has a length of one meter. So, $L_A = 1$ meter.

* We're watching it move by us and so our frame is H and the ruler's frame is Away and is moving at $u=0.5c$. 


How long does the meter stick appear to us in the Home, frame?

![galilean_train](meter_stick.png)



------

**The Answer:** 

The relationship for length contraction is the inverse of that for time dilation. We learned that the $\gamma$ for $\beta=0.5$ is $\gamma = 1.154$ and so we can directly calculate:

$$
\begin{align*}
L_H &= L_A/\gamma \\
&= \frac{1 \text{ meter}}{1.154} \\
L_H &= 0.87 \text{ meter}
\end{align*}
$$

It appears to us to be shorter by a little more than 10%.