Back to Discipline

0% Complete
0/10 Steps

In Progress
Skill 2 of 10
In Progress

# Cross-product

Right now we have two versions of the torque formula, $\tau=r_\perp\;F$ and $\tau=r\;F_\perp$, that include $\perp$-symbol, possibly sines etc. All we wanted was to ‘multiply the perpendicular parts’, so let’s invent a simpler single notation to mean just that:

$$\vec \tau=\vec r\times \vec F$$

The $\times$ is now our symbol for ‘multiplying the perpendicular part of one vector onto the other’ – let’s call this a cross-product.1

We could have chosen the cross-product to be $\tau=\vec r\times \vec F$, giving the magnitude of torque $\tau$. But we chose to invent it to also give the torque direction, so all is taken care of and we get the full $\vec \tau$. We can understand its direction with a new right-hand rule:2

Subscribe to valuable engineering skills for your resume or CV

Try full access with a 7-day free trial on all subscriptions.