Wrote general equation for a free body diagram

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Discussion Overview

The discussion revolves around the derivation of an equation for the net force and acceleration of a motorcycle on a flat surface, with implications for its applicability to other rolling objects. Participants explore the equation's validity and its limitations in various contexts, including irregularly shaped objects.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant presents an equation for net force and acceleration, suggesting it could apply to any rolling object.
  • Another participant questions the applicability of the equation to irregularly shaped objects, such as an apple, implying that a model would be necessary for accurate representation.
  • A later reply challenges the initial claim by stating that the equation may only be valid for objects with nearly perfect circular shapes.
  • Further discussion introduces the idea of using the equation for regular shapes like polyhedra and questions the implications of the equation's generality.

Areas of Agreement / Disagreement

Participants express disagreement regarding the applicability of the derived equation to various shapes of rolling objects. There is no consensus on the equation's validity across all scenarios discussed.

Contextual Notes

Limitations include the assumption that the equation can be applied universally to all rolling objects, which is challenged by the need for specific modeling for irregular shapes. The discussion also highlights the dependence on the shape and mass distribution of the objects in question.

Vodkacannon
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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 = Fp - μ*Fn - FD
Where: FP is the force of the bike acting against the ground, tangent to the ground
FD = [itex]\frac{1}{2}[/itex]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?
 
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Vodkacannon said:
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 = Fp - μ*Fn - FD
Where: FP is the force of the bike acting against the ground, tangent to the ground
FD = [itex]\frac{1}{2}[/itex]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?
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?
 
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:
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.
 

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