# Forces acting on a gyroscope base when trying to turn it

1. Jul 19, 2011

### refusenik

I am studying the influence of a gyroscopic effect of wheels/tyres on a steering system in a car. I can't seem to get my head around few concepts. It boils down to a simple problem.

Consider a free spinning gyroscope wheel with horizontally aligned axis.
This axis is mounted in a vertical fork style support that itself can rotate in a vertical fixed support. That's it.

If you imagine a bicycle with front wheel suspended above ground that's about right. The bicycle frame is attached to e.g. a wall but handlebar is free to rotate.

Now is the problem. Suppose the wheel has moment of inertia I around its horizontal axis and spins with angular velocity w. What I want to know is what extra effort would be required to turn the fork support around vertical axis with e.g. angular speed y.

I know that in this case the spinning wheel creates a moment acting on a fork support

M = I * w * y

but it is acting around horizontal axis (at right angle to the spin axis) and therefore is fully counteracted by reaction of vertical support (ball bearings.)

Will there be any extra effort required at all (compared to turning the same system with non-spinning wheel?)