I'm finding it hard to visualize that, and I don't remember noticing it when I last played with a bicycle wheel gyro (which was a long time ago, admittedly).But if you brace the gyro so that it's desire for the secondary tilt is stopped, you will not feel any unusual resistance to your initial tilting. It would feel as though the gyro is not spinning at all.
Yes. I have a gyro where the gimbal can be braced against a table to prevent any lateral turning. When I push it forward, the desire to rotate laterally is exactly opposed by a force from the table. It feels like it is not a rotating gyro at all -- just rotating forward with no unusual opposition.I'm beginning to get it -- I think -- based on adding the vector angular momentum that the new constraint would try to produce, on top of the original angular momentum of the spinning gyro. When we add the extra constraining torque, the resultant shows that the whole thing would tend to tip over.