also big discs have a larger moment of inertia which require a greater stopping force in itself
In general bigger discs have better braking power as the increase in moment of inertia is much lower than that of the mechanical advantage gained. Smaller discs are usually fitted as standard to cars as they're cheaper, lighter and relatively simple
**Question answered with effort below **
The term to answer your question though is Braking Torque
Braking Torque = Rotating Force x distance of pads away from centre
More technically:
The radius of the pads away from the centre is pretty self explanatory. You can have a massive disc brake, but if the pads are close to the centre, you dont gain anything (and waste alot of money) Obviously disc brake manufacturers dont do this, so dont worry
Force is slightly more complicated. As you can see from the diagram, the force acts perpendicular to the direction of rotation, but as you know the pistons act on the surface (or normal to the surface) with the equation
Normal Force = Applied Pressure x Area of pads
If you resolve forces on the disc, introducing the coefficient of friction μ, the frictional force (assuming perfectly normal to the surface, not toed in/out) is
Rotating/stopping Force = Normal force x μ
So the total torque that your brakes use IS:
Braking torque = Applied pressure x Area of pads x μ x distance of pads away from centre
So as you can see, just the pressure you apply on the brake pedal is not the only thing that changes the performance of the brakes. Pad material changes the coeffecient of friction μ, disc size as discussed alters the distance, and the pad size increases frictional area
Hope this helps