# How to prove inertial force is potential force.

1. May 11, 2014

### michaelexe

1. The problem statement, all variables and given/known data

Prove inertial force is potential force.

2. Relevant equations

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

3. The attempt at a solution
$$\oint \mathbf{F}_i\cdot d\mathbf{r}=0$$

2. May 11, 2014

### voko

What is "inertial force"?

3. May 11, 2014

### michaelexe

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

4. May 11, 2014

### michaelexe

inertial force

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

5. May 11, 2014

### 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.