Example Problem:

An air parcel at rest with respect to the
surface of the earth at the equator in the upper troposphere moves northward to
30N because of the Hadley Cell circulation. Assuming that absolute angular momentum is conserved, what
tangential velocity would the air parcel possess relative to the earth upon
reaching 30N?

(wr^{2})_{a} = (Vr)_{a} = [Vr +
(Vr)_{e}] = constant (1)

Note that w is positive if rotation is counterclockwise
relative to North Pole. Thus, V is
positive if the zonal motion vector is oriented west to east.

[Vr + (Vr)_{e}]_{f}
= [Vr + (Vr)_{e}]_{i} (2)

Solve for V_{f},
the tangential velocity relative to the earth at the final latitude.

V_{f} = __[Vr + (Vr) _{e}]_{f }–
[(Vr)_{e}]_{f}__

r_{f}

r = radial distance to axis of rotation = R cos ¿ (4)

V_{e} =WRcos ¿ (5)

Substitute (5) into (3) and
simplify by inserting initial V_{i }= 0

V_{f} = 482.7 km s^{-1}