Consider person 1at r1 trying to throw a ball to person 2 at r2 on a rotating platform. The velocity of the ball is a combination of the straight horizontal velocity person 1 throws it at, and the tangential velocity of the spinning platform (see orange arrows). As the ball is flying through the air, the two people continue to rotate with the platform. After some time (t) person 2 observes the ball to curve to the left of them a distance d (blue). Equating this distance to 0.5at^2 and solving for a, we find the Coriolis acceleration:
a=2ωv