I'm not a physics major or anything so I was hoping someone could explain this to me. How does the diameter of the brake disc effect the braking power giving the brake pad area is the same?

You would think the disc would be spinning at the same velocity no matter how far from the center it is. And wouldn't it require less force closer you get to the center of the disc?

 

One does not need to be a physicist sometimes... all we need is common sense ... There are 2 major things among others involved when braking is involved... Friction and urface area... I.e. if you'd take same rotor diameter and invent a circular break pad that would completely 'hug' entire rotor survce when breaking... and when utilize a batter 'grabbing' surface material i.e. with much higher friction coefficient - you'd stop the car in 20 feet vs. 120. Another question... would we need such fast stopping distance? I.e. would you enjoy the seat belt going through you every time we'd break like that ?
There is another inredient... a reasonably operating function... and the fact that break calipers/pads come as they are - is solely for production purposes... I've seen double-rotor/4 pads systems... which much improve braking distances... What current designs tell us.. they are sufficient enough...
One other to think about... you cannot implement too much of an improvement... since remember when 4 disks came out.. .? The 'drumed' cars scared the socks off you.. when you'd see them in the mirror.. UNABLE to stop in time... hence 'improvements' in braking shall occur very very gradually if at all ... i.e. stopping in 110 feet [on average] from 60.. is damn fast comparing to a quite recent past...