Why is a clockwise moment negative by convention?

Question

My physics book states that by convention a clockwise moment is said to be negative and an anti-clockwise moment is said to be positive. I'm curious about the origin of this convention.

My thoughts:

1. It doesn't matter which -wise you assign $+$ or $-$ as long as you are consistent.

2. In science being consistent with yourself is all well and good but for the purpose of communication it is convenient for everyone to be consistent with each other and hence to agree upon a convention.

3. Sometimes the reason why the convention was assigned as such is purely arbitrary and deserves no further discussion.

4. I have seen videos on YouTube where clockwise has been assigned positive and this seems more natural to me.

My question:

Is the above convention completely arbitrary or was there a reason for this assignment? If so what was the reason?

I have looked and could not find a satisfactory answer to my question anywhere.

Answer 1

We conventionally use a right-handed coordinate system in 3D physics, and in a right-handed system, positive moments are counterclockwise. You can show this starting from the definition of the cross product, which (in a sense) fundamentally sets the handedness of the coordinate system.

However, there's no physical reason to use a right-handed system. You could just as well do physics in a left-handed system, as long as you were consistent about it, and you would find that positive moments would be clockwise.

Perhaps there is a historical reason we use a right-handed system, but you'd have to ask about that on History of Science and Mathematics SE.