Coriolis Force

In a reference frame that is rotating at a constant relative to an inertial reference frame, there is a second inertial force named the Coriolis Force.  This force acts to deflect the body sideways. 

In the diagram above, a ball is being thrown by Ann at point A to Bill at point B with velocity v.  The platform is rotating counter-clockwise.  The ball also has a tangential velocity v_A = r_A due to rotation of the platform.  Bill at point B has a speed v_B = r_B due to rotation of the platform.  Because the Bill has a greater velocity, the ball will pass behind Bill. 

This is not the inertial force named centrifugal force because centrifugal force acts radially outward from the center.  This inertial force is acting sidewise.

Since F = ma, we can also use the term Coriolis Acceleration.  

r_B  -  r_A  =  vt                                  v, the radial velocity due to being thrown by Ann 

s_A  =  v_At                                      s_A, the displacement to the side by the ball

s_B = v_Bt                                          s_B, the displacement to the side by Bill

s = s_B  -  s_A  =  ( v_B   -  v_A )t          s, the displacement behind Bill.  How far behind Bill the ball passes. 

v_A = r_A   and v_B = r_B           Conversion between angular and translation velocities.  

s = ( r_B  -  r_A )t                          Substitution into earlier equation. 

s = vt²                                       Substitution of first equation into the last equation. 

s = a_cort²                                         Displacement with an initial velocity of zero. 

a_cort²  =  vt²                              Combine last two equations. 

a_cor  =  2v                                     Simplify previous equation. 

Because the Earth rotates, Coriolis Force has an effect on weather.  Without Coriolis Force, wind would flow directly from high pressure areas into low pressure areas.  With Coriolis Force, the winds are deflected to the right in the Northern Hemisphere creating counter-clockwise wind patterns around low pressure areas.  The winds deflect the opposite direction in the Southern Hemisphere. 

The Coriolis Force of Earth's rotation, is not a large force.  It has minimal effect on dense objects.  If a ball is dropped from a tall tower, the displacement to the East does exist, but it is small.  The reason it has an effect on weather is the low density of the air added to the large number of individual molecules affected.