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The problem when discussing this kind of thing is the distinction between torques and forces. The reaction arm is for the braking torque, the dropoput is for the braking force.
My brain goes a bit weird when I try to work out the forces in a braking system.
Draw yourself a free body diagram and it becomes a little easier. Could be some nice Wests entertainment if you fancy?
hamrack
My brain goes a bit weird when I try to work out the forces in a braking system. The brake resists the turning force of the wheel, which results in a reaction force at the dropout, but if the brake is essentially horizontal to the dropout (as in discs, drums and chainstay-mounted rim brakes) then that reaction force acts vertically (hence the issue of front wheels jumping down out of the dropouts on cheap forks with disc brakes). The force actually stopping the bike has to act horizontally, presumably as a reaction to the force exerted by the ground on the tyre.