Force diagram of a rider on a Ferris wheel: weight, seat force and centripetal acceleration around one turn.
The science
A rider moves on a circle of radius R at angular speed w, so the acceleration points to the centre with magnitude a = w^2 R. The seat stays level (the gondola hangs), so with the angle phi measured from the bottom the forces on the rider are weight mg and the seat force F, with F - mg = m a as vectors.
Vertically N = m (g + w^2 R cos(phi)): heaviest at the bottom, lightest at the top. Horizontally the seat back supplies -m w^2 R sin(phi). At the top the seat force reaches zero when w^2 R = g; faster than that the rider would leave the seat. For R = 25 m that needs 6 rpm, while real wheels turn at 0.03 to 1 rpm and the effect is a few percent of body weight.
Simplifications: constant rotation rate, a rigid level gondola without swing, no air resistance. Playback of one turn takes 12 s regardless of the real period. Checks: a finite-difference acceleration, the turn-average of the seat force (must equal weight) and the bottom-top difference 2 m w^2 R.