[gearhead2]

The following attached file is a free body diagram for a bicycle. Please excuse the crudity of the drawing, I drew it on paint. The bicycle weighs 100 kilograms with the rider on it and has 26 inch wheels. The bicycle is at rest. The static coefficient of friction between the wheels and the road is 0.5, thus making the force of friction 490Newtons. How would I calculate from here how much torque I would need to get the wheel to start turning and where exactly on the wheel (at what point on the wheel, be it the outside rim or on the hub where the gears are) would I need to apply that calculated torque?

[harum]

In theory, even a very small torque will get a bicycle rolling as long as this torque is enough to overcome friction torques created in bicycle bearings, which are usually near zero. Bearing friction torques are not related to friction created by tires.

[gearhead2]

So then how much to overcome to friction between the tires and the road?

[harum]

You don't overcome friction between tires and the road. This is what moves you forward. I was talking about friction inside bicycle gear. What weight should be attached to the outer rim of a wheel detached from a bike to make the wheel turning? It's almost nothing.

[gearhead2]

So then how would I calculate acceleration based on the torque applied to the wheel?

[gearhead2]

would it just be simply F=MA?

[harum]

yes. Except that you use an equation adjusted for rotational motion: T = I*Q, where T is torque, I - moment of inertia of a wheel, Q - angular acceleration. Angular acceleration is proportional to linear acceleration. I suspect though that the problem you are probably trying to solve takes a different approach, an easier one.