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Disc brakes work because you can use a much bigger lever to apply the frictional force - the pads can be set closer to the rotating surface, you can set the fulcrum closer, you can use a longer brake lever, you can use bigger pads etc...
It's our Greek friend all over again.
As Greenbank mentions, the force needed to slow the rotation of the wheel is negligible in comparison to the force required to slow the whole system.
Murphy's_Law
NotThamesWater
The smaller wheel requires more frictional force to brake (at the same rate) because of the smaller acting radius where the brake retards the rotating surface.
Archimedes, innit.