This may seem like semantics to you, but it is not.
The force exerted by air resistance is F = ½PV²Cdf
The force required to accelerate (overcome inertia) is F=MA
The equation that you have written below is the force required to accelerate an object horizontally through the air or other inviscid fluid in the absence of rolling friction and gravity. That situation is just never going to happen on a bike, and is just not applicable to any real situation. Therefore, I would say that the formula is useless as is.
Originally Posted by Ideologue
Air resistance at a given rate of acceleration: F = ½PV²Cdf + MA
Material science is one thing, basic equations are another. All I need is a kick-start back into the subject of physics. Determining component size, such as shaft wall thickness, to ensure they can cope with the forces they will be exposed to is relatively easy. Many equations exist and are easy to find (unlike the ones I am asking for help with) that can be used to determine critical component dimensions.
I also think that the equations that you are asking for help with are very basic fundamental equations that are discussed at various levels of detail in high-school and college courses. IMO, the equations that 'should' determine component size, shaft wall thickness, etc. are dramatically more complicated.
Also, you have not dealt with the rotational acceleration problem. This is also fairly easy (intro college physics course material), but significantly more complicated than what you are working on now. It also should not be neglected for a bike. That is why cyclists are more concerned with rotating mass (wheels) than mass on the bike frame.