# Wrote general equation for a free body diagram

1. ### Vodkacannon

39
So I derived this equation for the net force/acceleration of a motorcycle on a flat surface. I beleive this equation could practically be used for any rolling object.
ƩF = Fp - μ*Fn - FD
Where: FP is the force of the bike acting against the ground, tangent to the ground
FD = $\frac{1}{2}$pv2CDA (air drag)
μ*Fn is the frictional force of the tires, Fn is the normal force.

Now to find a:

ma = Fp - μFn - FD

a = (Fp - μFn - FD) / m

Is there anything wrong with this?

2. ### Simon Bridge

15,057
Woah! Let me turn down the volume a bit there:
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?

3. ### Vodkacannon

39
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.

Last edited: Nov 11, 2012
4. ### Simon Bridge

15,057
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.