Right-hand rule

‘Which way must I turn the bike wheel? Clockwise or counterclockwise?’ You can’t answer that because it depends on which side you look at it from.

Why don’t we invent a way to tell the direction. We have invented the vector version of angular properties: it points along the axis we are rotating about. But does it point leftwards or rightwards along this axis? Let’s quickly decide that

• if you are looking along with (the same direction as) the vector, the turning is clockwise, whereas
• if you are looking into (the opposite direction of) the vector, the turning is counterclockwise.¹

An angular-velocity vector now tells us everything about the turning:

• The vector magnitude tells ‘how much’,
• the vector location/tilting tells ‘about which axis’ and
• the vector direction tells ‘which way around’.

If you are given an angular property as a vector, it can be a bit hard to easily figure out, which turning direction it corresponds to. Let’s invent a simpler method that we can call the right-hand rule:

• Grab the vector with your right hand! Grab it so that your thumb points up along it.
• Then look at how your fingers curl around. The direction they curl in, that is the turning direction.