- Linear properties point backwards or forwards whereas
- angular properties “point”
*clockwise*or*counterclockwise*.

While the backwards/forwards feeling is *along *something – a direction that defines it – what is the clockwise/counterclockwise feeling? Isn’t it rather *around *something?

Around what? Grab the screwdriver and turn it. Aren’t you actually rotating about the screwdriver *itself*? If you imagine a line along the screwdriver, then this is the line the angular properties act *around*. This line *defines* an angular motion, like a direction defines a linear motion.

Why don’t we name this imaginary line: an **axis-of-rotation**.

It made sense to think of position, velocity, acceleration and force as vectors $\vec s$, $\vec v$, $\vec a$, $\vec F$. Their vectors point the same way as the properties themselves act. If you know the vector, you know ‘how much’ and ‘which way’. But when something is *rotating*, how can we invent a vector to point “the same way”? Should that be a “curved” vector or so?

No, why don’t we simply decide that an angular-property vector points along the **axis-of-rotation**? Then, when writing $\vec \theta$, $\vec \omega$ and $\vec \alpha$,

- the magnitude still tells ‘how much’ but
- the direction of the vector tells ‘about which axis’.

Naturally, ‘angular acceleration is change in angular velocity’, which is ‘change in angular position’, also in their vector forms:

$$ \vec \alpha= \vec \omega’\qquad\qquad \vec \omega = \vec \theta’$$

Whenever you see an angular-property vector, remember that this vector is imaginary and has just been invented to indicate the axis. It does not represent the turning itself. It *defines* the turning but doesn’t *represent* it directly. **Note** that this vector clearly is *perpendicular* to the turning direction (an angular property acts *around* its axis and thus its vector).