Inertial forces, relative strength, basic q.

[pepsimaxisgood]

The question is to rank the inertial forces, euler,coriolis and centrifugal in increasing order of strength, for a observer in the Earth' rotating frame, observing a body stationary in the UK.

My thoughts are that coriolis = 2mw X (dr/dt), and so depends on the velocity so can only come into play when there is motion.

A similar argument would hold for the euler force: m(dw/dt) X (dr/dt) . (Even without the dr/dt =0, my book says that dw/dt approximates zero, so this force would be zero anyway.

This would give the order : centrigufal, corilios/euler - with coriolis and euler tied.

However I'm not 100% sure dr/dt =0 - does this correspond to only translational motion?

(The question does not mention any of the forces being of equal strength, so I assume I am wrong somewhere...)

Thanks for your help guys !

 

[haruspex]

A similar argument would hold for the euler force: m(dw/dt) X (dr/dt) .

That's wrong (it's even dimensionally wrong). Try m(dw/dt) X r.
To answer completely, you'd have to investigate whether the Earth's angular rotation ever changes. If the Coriolis force is definitely zero here (I agree) then any nonzero Euler force will break the tie.