brakes, gears and leverage

Bicycle brakes squeal
at one time or another because they function by a stick-slip friction mechanism whose frequency is supposed to be out of audible range. When they make noise, it is most commonly because the pads generate caterpillar-like surface waves. Possible problems: new rim, gummy residue or wax or dirt on rim, excessively flexible (low quality) brake mechanism/calipers, glossy or sticky skin on new pad, rim out of true, old concave or damaged rim. Possible solutions: toe the brake pads in, clean rim with no-residue method (sheldon brown suggests abrasive scrubbing with household cleaner + rinse with water; alcohol works too sometimes), if caliper is low quality: maybe shortening the distance between arm and pad will help, change pads: if necessary use Kool-Stop pads, sand the pads to flatten them or remove residues,true wheel.

Toeing in: is preferred because a pad that makes full contact when it first touches the rim will rotate slightly because of frictional drag, which will in turn reduce contact and allow the pad to snap back and repeat the action. This causes surface waves in the pad and between the pad and rim, especially when the pad is new and thick. And this makes brakes squeal. When toed in, the pads contact the rim trailing-end first and develop full contact stably as pressure and frictional drag increase.

and 2 images:

Bicycle Totem 02, by Alain Delorme

French Ernestine Bernard in her race against a horse, in Toronto, in 1879
reported in National Police Gazette of June 28, 1879