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?
Hint
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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
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Some examples of vectors:
| position | |
| velocity | |
| force | |
| linear momentum | |
| angular momentum (could be new to you?) | |
| magnetic field (could be new to you?) | |
And some scalars …
| m | mass |
| v | speed |
| d | distance |
| ρ | density |
| R | resistance |
| T | temperature |
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
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!