How to prove inertial force is potential force.

AI Thread Summary
The discussion centers on proving that inertial force can be classified as a potential force, using the equation for potential energy, where inertial force is defined as F_i = -m*a. The attempt to demonstrate this involves integrating the inertial force over a closed path, resulting in zero, which raises questions about the nature of inertial force itself. Participants express confusion regarding whether an arbitrary force can be considered potential, indicating that proving the potential nature of inertial force may not be feasible. The conversation highlights the complexities in defining forces and their classifications in physics.
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Homework Statement



Prove inertial force is potential force.

Homework Equations



$$\mathbf{F}_i=-\nabla V_i$$

The Attempt at a Solution


$$\oint \mathbf{F}_i\cdot d\mathbf{r}=0$$
 
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What is "inertial force"?
 
$$\mathbf{F}=m\mathbf{a}$$
$$\mathbf{F}-m\mathbf{a}=0$$
$$\hbox{inertial force}\mathbf{F_i}=-m\mathbf{a}$$
$$\mathbf{F}+\mathbf{F_i}=0$$
 
inertial force

$$\mathbf{F}=m\mathbf{a}$$
$$\mathbf{F}-m\mathbf{a}=0$$
$$\hbox{inertial force}\mathbf{F_i}=-m\mathbf{a}$$
$$\mathbf{F}+\mathbf{F_i}=0$$
 
That is not making any sense. If ##F## is an arbitrary force, then ##F_i## is also an arbitrary force. Are you required to prove that an arbitrary force is potential? That won't work.
 
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