1. Time dilation recap:
A rocket travels at 0.75c and covers a total distance of 15 light years. Answer the following questions, explaining your reasoning:
What are the two frames of reference being compared here?
The frame of reference of the pilot and the frame of reference of observers on Earth
How long is the journey time from the frame of reference of Earth?
Speed = distance / time = 15/0.75 = 20yrs
What part of the formula is represented by the total journey time from the pilots frame of reference?
t0 because it is the smaller value
Calculate how long the rocket is away from Earth from the frame of reference of the pilot.
20 = t0 (1 – 0.752)-0.5 =

2. Length contraction
What happens to the length of moving objects as they approach the speed of light?
How can we modify the Lorentz factor to accommodate this in a formula?
You should be able to use this relationship to calculate contracted length

3. So objects get shorter as they approach light speed:
If we were to replace the letter t with L, so L0 represents proper length and L is the contracted length, how would this formula look?

4. Length Contraction
Another consequence of the invariance of the speed of light is that an observer measuring a rod moving parallel to its length will find that it is shorter relative to its stationary length. In effect if you measure a moving car, you will find that it is shorter than the stationary car. This effect is called length contraction.
As with time dilation, the change is so tiny as to be negligible. But this is not the case for objects moving close to the speed of light.
The relationship is:
The term l0 is the proper length as measured in the frame that is at rest relative to the object.
The term l is the length as measured by an observer in a frame of reference that moves at a constant relative velocity of v.

5. Length contraction problem
My ladder is 5m long. It does not fit in my garage when it is at rest as my garage is only 4.5m. How fast would the ladder need to be travelling in order to fit in my garage?
Step 1 – Identify which values are L and L0
Step 2 – Rearrange the equation