What is the Coriolis Effect?

It seems to us that we are stationary on earth, but the earth is in fact rotating about its own axis, as well as revolving around . So to observers in a different frame of reference example in space, it will seem to them as though a centripetal force directed towards the centre of the circle is keeping us in circular motion, which is in fact the case, but to us, we feel as though a fictitious outward force is pushing us away from the centre of the circle.

Think of when you round a bend at a high speed in a car - The centripetal force directed inwards keeps you in a circular path, but you feel as though you are being pushed wide outwards and this fictitious force is called the Coriolis force.

In terms of polar co-ordinates, we can define a position unit basis vector ##hatr=(costheta)hati+(sintheta)hatj## in the direction of the radius of the circle and an angular basis unit vector ##hat theta=-sinthetahati+costhetahatj## in the direction of the vector cross-product between ##vecr and vecv##, ie in the direction of ##vecomega##. Then we can define the position of a particle by ##vecr(t)=r hatr ##. Then the velocity is ##vecv(t)=(dvecr)/(dt)=dotrhatr+rdotthetahattheta## Then the acceleration is ##veca(t)=(dvecv)/(dt)=(ddotr-r(dottheta)^2)hatr+(rddottheta+2dotrdottheta)hattheta## The last term in this expression represent the Coriolis acceleration of the particle.