This post is the second in this series. You can read the background on this series in my previous post. I hope the questions in this series promote some discussion of what the goals of contemporary introductory physics should be these days.
Here is the next question. It has multiple parts.
In one sentence, explain what we mean when we say a physical quantity is constant. In one sentence, explain what we mean when we say a physical quantity is invariant. In one sentence, explain what we mean when we say a physical quantity is conserved. Give an example of a physical quantity that is constant, invariant, and conserved. Give an example of a physical quantity that is invariant, but not necessarily conserved. Finally, give an example of a physical quantity that is conserved, but not necessarily invariant.
It is important for students to understand the distinctions among these three terms (constant, invariant, and conserved). They are not interchangeable and using them correctly requires a rather deeper understanding than students usually get. As I said last time, I won’t disclose answers here but feel free to kick things around in the discussion area.
Go!
I have to admit that I don’t think I ever even use the word invariant when I am teaching introductory physics. Am I doing it wrong?
Wrong? That’s your call. I think invariance is an important concept to understand within the contexts of vector analysis and relativity, two frameworks that are important to contemporary physics. If your course doesn’t include these frameworks then there may indeed be no real need for the concept.