Those spider/octopus/monster rides operate under the same principle as the Tilt-a-Whirl. The car sits on a rotating axis, just enough off-center that as the ride rotates, it creates centrifugal force, since the car itself is free to rotate separately from the other rotational force (I'm not a physics person, so I apologize if I'm getting the terms slightly off).
At the same time, the rotation of the central arms also generates centripetal force, which works to keep the car moving on the same circular track as the main ride. Since centrifugal force isn't really a "force" as much as the inertia of motion (An object at rest stays at rest), the trick is to get the car in motion in a way that complements both the rotational force of the central arms and the effect of gravity and centrifugal force operating on the car in the midst of the rotation. You have to break the car's inertia and let it work against the centripetal force created by the rotation of the arms.
In other words - you have to coordinate with the other adult riding on the ride . http://sinoamusementrides.com/octopus-ride-for-sale/. Those other people in the other cars are usually working their butts off to get their car spinning. When you get into motion, start leaning in a direction and shifting your weight, as it changes the center of gravity (somewhat) on the car itself.
When the car starts to move, follow through in that and let your weight add to the downward motion of the car. At some point, centripetal force works against you and the car will reverse direction, so follow it. Usually, it'll start a kind of pendulum effect (like the Pirate ship ride) and you will be able to get some good spinning out of your car.
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