### Inertial and noninertial reference frames

see Fig.1.

If we define the axis and

as in Fig. 1, then we can write the velocity vector of the river as:

since

, we have that the coriolis correction to the acceleration vector is

Now observe at Fig. 2.

it shows a cross-section of the river, as it flows towards you. convince yourself that the new

x'
axis, which is pointing towards the left bank of the river, is the same
as the previous x axis, so the river feels coriolis' acceleration

also, it feels an acceleration downwards, we'll naturally call it

g, which is comprised of the gravity acceleration and a small, insignificant, centrifugal correction. so we have

and now we'll argue that