# B Why is force vector F but acceleration vector a not A?

1. Nov 5, 2018

### TheCelt

Is there some rule or standard that determines whether we define a vector with upper or lower case? I have not been told of any particular rule but it seems with velocity and acceleration they are lower case but force has always been upper case from what I've been reading so far.

Is there a rule to it?

2. Nov 5, 2018

### Staff: Mentor

There are far more quantities than letters, so they are used in multiple ways. It's the context - if at all - which gives some standard notations. Yes, acceleration and velocity have usually lower case letters and Force an upper case. But think about that they are in conflict with Ampère, Volt and frequency. All these have presumably historic reasons. It's similar in math: vectors are usually written as $u,v,w$, but if you have groups and vector spaces at the same time, then it's convenient to write $U,V,W$ and reserve the lower case letters for the group elements.

The only thing for sure is, that $f=A\cdot M$ or $u=r\cdot i$ will raise a lot of questions.

Last edited: Nov 5, 2018
3. Nov 5, 2018

The letter $A$ is usually used for area. Similarly, $V$ usually means volume, or electrical voltage, while $v$ means velocity. The letter $T$ is usually used to represent the period of oscillation or some other specific time, while the letter $t$ indicates a running time.

4. Nov 5, 2018

### Staff: Mentor

... and $T$emperature.

5. Nov 5, 2018

### Staff: Mentor

I remember a discussion I once had about the justifications of standard notations. We could write $F=m \cdot a$ as well as $\Phi = B \cdot \aleph\,$ - a Greek 'F', a Cyrillic 'W' and a Hebrew 'a'. What an incredible chaos would break lose. The discussion I mentioned was about matrices: why $a_{ij}$ and not $a_{ji}\,?$ Well, because $a_{ji}$ would be the transpose. It makes sense in a way, although there is no logical reason for it.

6. Nov 5, 2018

### DaveE

Basically, no. Different people have different rules (i.e. notation schemes), sometimes the same people use different notation in different situations. It is a problem you will have to deal with through out your career in the physical sciences. This is why it's important to help out people reading your work by making it clear what your notation means.

7. Nov 6, 2018

### sophiecentaur

The 'rules' are very local and they have to be different for handwritten work.