# Using Vector Notation in Physics: Appropriate or Wrong?

• tomwilliam
In summary, it is generally not appropriate to use bold notation for vectors in equations involving energy or momentum, as only the magnitude of these quantities is needed. However, if there is a need to distinguish between a scalar and vector quantity, a more verbose notation may be used. The standard usage in texts and journals is to use unbolded symbols to denote the magnitude of a vector.
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

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

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.")

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.

Thanks all.
Much appreciated.

## 1. Is vector notation necessary in physics?

Yes, vector notation is essential in physics because it allows us to represent physical quantities that have both magnitude and direction. Without vector notation, it would be difficult to accurately describe and solve problems in physics.

## 2. What is the difference between vector and scalar quantities?

Vector quantities have both magnitude and direction, while scalar quantities only have magnitude. For example, velocity is a vector quantity because it has both speed (magnitude) and direction, while distance is a scalar quantity because it only has magnitude.

## 3. Can vector notation be used in all branches of physics?

Yes, vector notation can be applied in all branches of physics, including mechanics, electromagnetism, and thermodynamics. It provides a standardized and efficient way to represent and analyze physical quantities in various contexts.

## 4. Is it appropriate to use vector notation in introductory physics courses?

Yes, it is appropriate to use vector notation in introductory physics courses. While it may seem intimidating at first, learning and understanding vector notation is crucial for mastering the fundamentals of physics and building a strong foundation for more advanced concepts.

## 5. Are there any common mistakes beginners make when using vector notation in physics?

One common mistake is confusing vector quantities with their scalar components. For example, velocity is often mistakenly equated with speed, when in reality, velocity is a vector quantity that also includes direction. It is essential to understand the difference between vector and scalar quantities to use vector notation correctly.

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