The first photo shows the orientation of the riders at the start of the ride, when the circle is in a horizontal plane. The second photo shows the orientation of the riders when the circle is in a vertical plane, with sufficiently large acceleration to keep the gondola upside down in the highest point. 

Consider first the situation when the circle moves in a horizontal plane.

A few questions to consider before looking at the graphs showing how the angular velocities vary over time.

1. As the ride starts to move, the z axis of the riders point straight up, and the rotation is also around a purely vertical. Is this rotation around the z axis ("yaw") in the positive or negative direction?
2. When the ride is moving, the gondola rotate around their suspension axes, which is also along the x-axis of the rider, leading to a "roll". Is this roll in the positive or negative direction
3. When the circular motion is in the vertical plane, i.e. around a horizontal axis: what is the type of rotation as seen from the system or the rider. (Is the rotation positive or negative pitch, yaw or roll?) Look at the second photo, above, and refer to the photo showing definition of the x, y and z axes)
4. The initial roll causes the main rotation to contribute both to yaw and pitch. Will this pitch contribution be positive or negative? (Hint: Compare to the full roll rotation which leads to the situation in 3)
5. What angular velocity is required to the the centripetal acceleration found on the previous page? 

The graphs below show the axes of the rider together with the direction of the main rotation of the ride. 

You may also want to look at drawings of the relevant coordinate axes when the ride moves in a horizontal plane (until about 30 s in the graphs) and when it moves in a vertical plane during the middle part of the ride.