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Correction and Hint for Homework 4, Problem 2
Dear PHYS 521 students,
I should mention that the number given for the Earth's rotation
angular velocity omega in HW 4, Problem 2 is wrong. It is about
7.3 x 10^{-5} rad/s and NOT 2.0 x 10^{-4} rad/s as stated in that
Qualifier problem. Please use the correct number in calculating
your answer.
By the way, you may take Bahamas Grand Bank to be due
east of Miami. Because the northerly water flow is deflected
to east by the Coriolis force, it tends to "sweep" water higher
toward east. If there were no flow, then this would be level
instead. The physics of this problem becomes clearer if you
focus on small mass of water at the surface of the sea. The
(real) forces acting on this mass are the gravity and normal
force. Then, as viewed in the Earth frame, there will be the
fictitious forces including the Coriolis force. You will find that
the Coriolis force is the cause of the ocean tilting upward
toward east, or rather, downward toward west (Miami). The
force balance will give you the angle of this tilt.