### Example: Deflection of a Falling Object

If we drop an object from height , the effect of the centrifugal force is already in the local value and local direction of . The Coriolis force is not included and it is proportional to velocity so it will not affect the direction of plumb bobs. The Coriolis force will cause a deflection from a vertical path as the object falls. Lets call the direction the local upward vertical. We need to pick two directions perpendicular to that to form a coordinate system. We can choose the direction be be north and then we must choose east to be in the direction to have a right handed coordinate system.

For a downward velocity, the Coriolis acceleration is to the east,

where will be a negative number.

One can integrate this equation to find the deflection when a cannonball is dropped from a height .

For a height of 100 meters, at 32 degrees latitude, the displacement is about 1.9 cm. Explain why the deflection is always to the east.

Jim Branson 2012-10-21