i understand the reason and steps leading to the equation that relates acceleration in the inertial frame to acceleration in the rotating frame i.e. a(I) = a(R) + 2(omega)Xv(R) + (omega)X(omega) X r a(I) = acceleration in inertial frame a(R) = acceleration in rotating frame omega = rotation vector X = cross product v(R) = velocity in rotating frame r = position vector now i understand why this (or a rearrangement thereof) can be applied to a system like focaults pendulum, becuase you have acceleration going on, so obviously you would want to relate the changes between the two frames. however, everyone remembers the simple problems where you simply use the coriolis term to calculate the direction and magnitude of the coriolis force on something like a moving train (i.e. 500 tonne train moving north at 100kph experiences a coriolis force of something liek 1500N eastwards) however it struck me, that if the train is moving with constant velocity, then surely the above equation doesnt apply? and surely the equation linking the two vectors a together is simply the very original relation between the two frames for vector that is fixed in the rotating frame namely: V(I) = V(R) + omega X (V(R)) or is it more subtle than this?