How to prove inertial force is potential force.

[michaelexe]

Homework Statement

Prove inertial force is potential force.

Homework Equations

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

The Attempt at a Solution

$$\oint \mathbf{F}_i\cdot d\mathbf{r}=0$$

 

[voko]

What is "inertial force"?

 

[michaelexe]

$$\mathbf{F}=m\mathbf{a}$$
$$\mathbf{F}-m\mathbf{a}=0$$
$$\hbox{inertial force}\mathbf{F_i}=-m\mathbf{a}$$
$$\mathbf{F}+\mathbf{F_i}=0$$

 

[michaelexe]

inertial force

$$\mathbf{F}=m\mathbf{a}$$
$$\mathbf{F}-m\mathbf{a}=0$$
$$\hbox{inertial force}\mathbf{F_i}=-m\mathbf{a}$$
$$\mathbf{F}+\mathbf{F_i}=0$$

 

[voko]

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.