# Vectors or not?

#### tomwilliam

I have a general question on presenting physics work:

When is it appropriate to use vector (bold) notation? I understand the difference between vectors and scalar quantities, and always used to think an equation with a vector on the LHS needed to have a vector on the RHS, but in writing up a recent question, had this equation:

E$$_{kin}$$=1/2mv$$^{2}$$

which I then use to produce an equation involving momentum, p, and then the final result which is a dimensionless quantity.

Now I know energy is not a vector quantity. Does that mean it is wrong to put the velocity reference in bold?

The same goes for the expression involving momentum:

E$$_{kin2}$$=(p$$^{2}$$)/2(m+M)

is it wrong to have the p in bold?
Tom

#### D H

Staff Emeritus
[Equation corrected]
$$E_{kin}=\frac1 2 \,\frac{p^2}{m+M}$$

is it wrong to have the p in bold?
In my opinion, yes. If you want to use a vector you would need to be a bit more verbose:

$$E_{kin}=\frac1 2 \,\frac{\mathbf p\cdot \mathbf p}{m+M}$$

or

$$E_{kin}=\frac1 2 \,\frac{||\mathbf p||^2}{m+M}$$

The only time you need to be verbose like that is when you are already using (in this case) a scalar p that denotes something other than the magnitude of the momentum vector. Otherwise, use of a unbolded symbol, particularly when squared, indicates the magnitude of the corresponding vector. It's pretty clear, and that is the standard usage in texts and journals. (Suppose you write a paper in which p denotes momentum but p denotes pressure. This paper will probably come back with some scathing review comments along the lines of "Don't do that! You confused me, and I know the subject.")

#### Doc Al

Mentor
In an expression for KE, I would not use bold (or any other notation) to represent velocity or momentum as vectors, since only the magnitudes of those quantities are needed.

Realize that: $$v^2 \equiv \vec{v} \cdot \vec{v}$$

Edit: While I was daydreaming, D H beat me to it.

#### tomwilliam

Thanks all.
Much appreciated.

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