How Do Position Vectors Differ in Inertial and Rotating Frames?

[aftershock]

Homework Statement

Homework Equations

F_rotating = F_inertial + F_cor + F_cf

The Attempt at a Solution

For the inertial field: F = -qv x b -kQq/r²

For the rotating field it would be the same term plus the coriolis and centrifugal forces.

The issue I'm having trouble with is this:

The v in qv x b has to be the derivative of the position vector drawn from the inertial field right? But the position vector and its derivatives in the coriolis and centrifugal force formulas are drawn from the rotating frame right? So I can't just use one r for all the terms.

But in the solution http://www.physics.umd.edu/courses/Phys410/gates/Phys410_Solution_06.pdf it looks like that's exactly what was done... just one r?

I can't make sense of this, can anyone shed some light on it?

 

[TSny]

For the inertial field: F = -qv x b -kQq/r²

For the rotating field it would be the same term plus the coriolis and centrifugal forces.

The issue I'm having trouble with is this:

The v in qv x b has to be the derivative of the position vector drawn from the inertial field right? But the position vector and its derivatives in the coriolis and centrifugal force formulas are drawn from the rotating frame right? So I can't just use one r for all the terms.

Right, the v in the magnetic force qv x B is the rate of change of the position vector relative to the inertial frame. However, you can express the rate of change of the position in the inertial frame in terms of the rate of change of the position in the rotating frame and in terms of $\Omega$. But note that the magnitude of the position vector, r, is the same in both frames. So, you don't need to worry about the r in the Coulomb force.