Q1.3 Thinking about vectors (T)

Give six examples of physical quantities that are vectors and a further six examples that are scalars.

Identify three respects in which vectors differ from scalars.

Do you think time is a vector or a scalar?

Hide

Hint

You should be able to dredge up enough examples from your memory banks. Otherwise you’ll need to browse through HRW, which would be a good thing to do anyway.

The very last bit is to allow you to stretch your imagination a bit.

 

Solution

Reveal
Hide

Solution

Some examples of vectors:

$\vec{r}$position
$\vec{v}$velocity
$\vec{F}$force
$\vec{p}$linear momentum
$\vec{L}$angular momentum (could be new to you?)
$\vec{B}$magnetic field (could be new to you?)

And some scalars …

mmass
vspeed
ddistance
ρdensity
Rresistance
Ttemperature

Some differences between vectors and scalars:

  • Well I expect everyone would write down that a vector has a direction associated with it, while a scalar does not.
  • A bit more generally you could say that a vector carries more information than a scalar (that’s why it needs 3 numbers to specify a 3D vector, and only one to specify a scalar).
  • So when we add vectors together we are really adding together the corresponding components: there are three additions to do for 3D vectors.
  • We can multiply vectors together in either of two ways, both of which are quite different from the way we multiply scalars.
  • We can never equate a vector to a scalar; any equation that does this is WRONG. If you write down an equation beginning $\vec{A}= \ldots$ then the right hand side must also be a vector which matches the LHS in magnitude and direction.

Is time a vector or a scalar? I put this in to encourage you to muse a little. I’d say it is best thought of as a one-dimensional vector. When we study kinematics we find ourselves using t to label an axis, just like x or y. Though most of us tend to believe we can ‘travel’ only one way along the t-axis!