Query about gearing...

[Tony Press]

 It always confuses me when I’m told friction is a function of perpendicular force not area of friction material.  Theoretically 1” brake shoes should perform the same as 1 1/4” shoes. But that doesn’t seem to be the case in practice.

It always confuses my students as it did me as a student in the 'seventies.The formula for simple friction force, f = mu x N, where mu is the coefficient of friction and N is the normal (i.e. right angle) force. You can get into more complicated formulae but.....

A 1" wide shoe will produce the same friction force as a 1 1/4" BUT the force has to be the same, that's the catch! (And mu has to be the same, which is a different argument)

The real benefit is that a 1 1/4" shoe dissipates heat better so less prone to fade although, subjectively, they do seem to work better and defy the mechanics lesson.....

My late uncle, chief engineer at a large engineering company. always claimed that friction couldn't be independent
 of the area of contact, citing the difficulty in separating interleaved telephone books.

But if I remember this is in fact due to the normal force being multiplied