Lesson 5: Length Contraction
We have seen that time is not absolute since it depends on the frames of reference of observers so it makes sense to question whether length is also not absolute. Length contraction is a phenomenon, like time dilation, which occurs in the direction of motion. This phenomenon of length contraction is also called a Lorentz contraction.
The central concept of this chapter is to understand that length contraction is a phenomenon similar to time dilation in the field of special relativity.
Learning Objectives:
The following thought experiments can be used to conduct a Think, Pair, Share to introduce the topic of time dilation:
The central concept of this chapter is to understand that length contraction is a phenomenon similar to time dilation in the field of special relativity.
Learning Objectives:
 Understanding that proper length is the length of an object measured by an observer who is at rest relative to the object.
 Knowing that length contraction occurs only in the direction of motion.
 Being able to derive the formula for length contraction and using it appropriately.
The following thought experiments can be used to conduct a Think, Pair, Share to introduce the topic of time dilation:
 The class has seen that time is not absolute since it depends on the frames of reference of observers. What do you think might happen in the case where length is not absolute?
 Assume a cylindrical spaceship 10 m in diameter is moving past Earth at high speed, what would it appear to look like in the frame of Earth and in the frame of an occupant inside the spaceship? Would the diameter change?
Click the link below to be directed to a tutorial which discusses how relativistic length contraction must follow from time dilation.
Click on the link below to go to a simulation that explains the Twin Paradox as an example of the relativistic Doppler effect.
You might wish to share the fact that time is known as the fourth dimension and that an event can be described by 3 quantities that depict where it is in space and a fourth to describe where it is in time. Students may find it fascinating to know that when objects move at speeds near c, space and time become intertwined. You might also wish to perform the following experiment for a reallife demonstration of length contraction: 
The video below shows the techniques that can be used to solve a length contraction problem.

The following video uses a tube as the "clock" to explain both time dilation and length contraction.

As a way of ending the class, I encourage doing the following:
 Tell students that the fourth dimension is time and that an event can be described by 3 quantities that depict where it is in space and a fourth to describe where it is in time.
 Ask what might happen to space and time when objects move at speeds near c and to check their answer online for homework.
 Point out that you will choose a student randomly next class to provide the class with the answer.
References
 Hirsch, A., Stewart, C., Martindale, D, & Barry, M. (2011). Nelson Physics 12. Toronto: Nelson Thomson Learning