I was thinking about the problem set I just assigned and I realized (for the first time?) that cross product is not associative! Hahaha it only took me 27 years of teaching this.
q (v x B) x B \\ne q v x (B x B)
#nyuphysics2

(I feel like it has something to do with the fact that the cross product operator can switch vectors to pseudo-vectors and vice versa.)

- if r, v are vectors, r x v is a pseudo-vector, as is v x r
- if B is a pseudo-vector, v x B is a vector, as is B x v
- if Ω is a pseudo-vector, Ω x B is a pseudo-vector, as is B x Ω

did I get that right?

You can understand the difference between a vector and a pseudo-vector by asking yourself: Do I need to pick a hand-rule (like right-hand rule) to make a prediction about an observable using that object?
- momentum p: No.
- magnetic field B: Yes.

thank you for listening to my Ted talk.
(that was my first-ever thread)