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

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.

 

[PJC01]

I would say that your equation looks accurate and comprehensive for describing the net force/acceleration of a motorcycle on a flat surface. It takes into account the various forces acting on the motorcycle, including the force of the bike itself, friction from the tires, and air drag. I agree that this equation could potentially be applied to other rolling objects as well, as long as the factors such as air resistance and friction are considered. However, it is always important to test and validate any equations through experimentation and observation, as there may be other factors at play that could affect the motion of the object.