# The Angle Windmill

One of the places I would always fall down in A-level mechanics was on inclined plane force diagrams: I was chronically incapable of putting the correct angle in the correct place.

Until, that is, I figured out…

### The Angle Windmill

It looks like this:

The process goes as follows:

- Draw a big diagram without any forces on
- Mark the angle between the plane and the horizontal as $\alpha$

- Draw a line perpendicular to the inclined plane (in grey on the diagram) through your object
- Draw a horizontal and vertical line (in green) through the object
- (You now have eight rays coming out of the object
- Find and mark a pair of rays separated by $\alpha$
- Mark alternate spaces between rays with $\alpha$

Boom! Job done. Now you know which angle goes where. You might alsonote that the angles in the gaps are all $90º - \alpha$.

### But wait. There’s more.

Suppose you need to resolve a force that lies on one perpendicular grid to the other.

If you draw the **s**ails on the windmill like this, it tells you which component of the force you’re resolving requires a **s**ine.

This is, of course, a lazy shortcut – working out the trig isn’t *that* hard. It’s just easy to get wrong in a hurry, and I was always in a hurry.

(You may like, as an exercise, to convince yourself that all of the assertions in this post are true.)