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.