Wrote general equation for a free body diagram

[Vodkacannon]

So I derived this equation for the net force/acceleration of a motorcycle on a flat surface. I believe this equation could practically be used for any rolling object.
ƩF = F_p - μ*F_n - F_D
Where: F_P is the force of the bike acting against the ground, tangent to the ground
F_D = $\frac{1}{2}$pv²C_DA (air drag)
μ*F_n is the frictional force of the tires, F_n is the normal force.

Now to find a:

ma = F_p - μF_n - F_D

a = (F_p - μF_n - F_D) / m


Is there anything wrong with this?

 

[Simon Bridge]

So I derived this equation[/size]

Woah! Let me turn down the volume a bit there:

... for the net force/acceleration of a motorcycle on a flat surface. I believe this equation could practically be used for any rolling object.
ƩF = F_p - μ*F_n - F_D
Where: F_P is the force of the bike acting against the ground, tangent to the ground
F_D = $\frac{1}{2}$pv²C_DA (air drag)
μ*F_n is the frictional force of the tires, F_n is the normal force.

Now to find a:

ma = F_p - μF_n - F_D

a = (F_p - μF_n - F_D) / m


Is there anything wrong with this?

So you'd use this for something like a rolling ball? I guess you'd factor in the mass-distribution in one of the F's there ... that is pretty general indeed. How about for irregularly shaped objects like an apple?

 

[Vodkacannon]

Your kidding. Irregulaly shaped objects like apples?
Well you would need to run a model of a 3D apple through a simulator. There can't possibly be an equation to model that.
My bad, that's why you can't use this for every rolling object. Only for surfaces that are nearly perfectly circular.

 

[Simon Bridge]

How about a regular shaped object then, like a polyhedron?
A hollow sphere with another, much smaller but heavy, solid sphere free to roll inside it?
You did claim that the equation could be "used for any rolling object".
You asked "in there anything wrong with this?"
Now you know.