how do rider in ferris wheel possess translatory but not rotatory motion?
Because they hang from a bar that allows them to maintain their orientation by rotating about that axis.
I rode, once, on a wheel where the individual cars were pivoted near their CM. There was a clutch control that allowed you to grip onto the pivot . You could go round a 360 degree trip and the car would also rotate by 360. Very unpleasant, aamof. It was very difficult to avoid getting the car 'tumbling' due to coupling with the big wheel.
The above image is of a conventional wheel, which is pretty stable to ride in because, as BvU sys, the cars hang with their CM well below the pivot. The London Eye is a large Ferris Wheel on which the cars are mounted 'actively' to keep them above the wheel, at the top of the flight. This gives a better view. Each car rotates within its mounting, to keep the floor in the right place - it's very stable feeling and is obviously driven and held in a vertical position all the way round.
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