00:01
In special relativity, lengths along the direction of motion get contracted by the lorentz contraction factor gamma.
00:15
So if you are in the frame moving with the object, you do not see the contraction.
00:21
But if you are standing by watching it move with relative motion, the direction, the length along the direction of motion is.
00:32
Contracted.
00:34
So here we have a rod that's moving by, and it's moving quite quickly with a velocity of 0 .995c.
00:42
So we will go ahead and calculate the gamma factor and then talk about how this object appears different in the frame of it moving by, as opposed to its proper frame.
00:59
So gamma, by the way, is 1 over the square root of 1 minus v over c squared.
01:08
And we usually see the velocity given as a fraction of the speed of light.
01:14
So working this out, this gives us a gamma of about 10 to three significant figures.
01:23
So the thing to realize is that we can break up this picture into two separate components.
01:30
The component along the direction of motion, and that is an amount contracted.
01:41
So it has length l -0 divided by gamma along the perpendicular direction, whether you call that y or z.
01:50
It doesn't matter.
01:52
But that has exactly the length that it would have, even in the proper reference frame, moving with the rod.
01:59
So we can simply take the x and y components of the rod in our moving frame and figure out what these two sides are.
02:13
So l -0 is equal to 2 meter times sine of 30, and that's just one meter.
02:25
L -0 over gamma is, let's see, let me give some space here...