Coriolis force is responsible for the formation of hurricanes.

When a low pressure region forms, air particles move in, and the Coriolis force bends them:

Each molecule of air in bent clockwise in the northern hemisphere [by the right hand rule with going into the plane], which leads to an anticlockwise swirling motion.

In the southern hemisphere, the Coriolis force bends particles anticlockwise, leading to a clockwise swirling motion.

Motion along the Earth’s surface is not in general perpendicular to the axis of rotation . Hence, the effect of Coriolis force is typically weaker near the equator. There are empirical observations that hurricanes do not form within near the equator.

[ can be substantial near the equator if moves along the equator, but it pushes particles vertically, and it need to compete with gravity, which is much stronger.]

Consider dropping a ball from a tower on the euqator. We will consider where the ball lands.

Initially,

As the ball falls, the distance to the axis decreases, so the angular velocity must increase to conserve angular momentum.

At the foot of the tower, , which must give , and hence the ball rotates faster than the Earth, so it lands slightly east of the foot of the tower.

In the rotating frame,

[We can neglect the centrifugal force since it does not affect the horizontal motion.]

Integrating once gives

where is the initial position of the ball. Subsituting Eq · 358 into Eq · 357 gives

The last term acts in the vertical direction and is small, so we can neglect it. Hence, integrating twice gives

Consider the following right-handed set of basis:

Then, substituting back into Eq · 360 gives

Clearly, is negative at positive , so the ball lands slightly east of the foot of the tower.