Car gyroscopic effect problem/doubt

[Shivanand]

Problem Statement

Suppose a car has mass M. It has a flywheel with axis running from front to back between left and right set of wheels. Let the flywheel have moment of inertia I and let it rotate clockwise at a constant angular velocity of w (omega). The flywheel shaft is held inside two bearings (front and back and it turns clockwise as seen from back of the car. Assume the shaft is massless (See the attached image).

1) If the car is not on road and in free space (vaccuum), if jets are fired from left-front and right-rear corner so that there is a torque tending to steer the car right, can the car steer or does it precess in vertical plane? If it steers, what is the minimum angular velocity of the flywheel to prevent the steering motion?

2)If the car is on road and it is heavy enough to stay in contact with road at all times, and it tries to take a right turn (steer right). The bearings are strong enough to prevent the flywheel from precessing in vertical plane. So the flywheel essentially is not allowed to precess. Will there be any resistance for the steering motion?



My attempt at solution

1) For the first problem I think the car cannot steer due to the jets and just precesses along with the flywheel in the vertical plane.

2) For the second problem I think no resistance is offered for the turn.

Am i right? If I am not could you please correct me? I would be glad to read your responses and ideas.

 

[K^2]

1) Correct, it will just precess. The angular momentum vector points along the length of the car. The only source of torque are your two jets, and that torque is perpendicular to the angular momentum, so the angular momentum vector will rotate around axis perpendicular to the wheel axis. (I'm just using the later to denote direction. They have nothing to do with the physics.)

2) The car will seem "heavier" in the turn. It will also "try" to tilt forward or backwards, which you'll notice if there is suspension.

 

[Shivanand]

Hi,

Thanks for the quick reply..

If there is no suspension (or stiff suspension) and the car is rigid and does not allow any sort of rotation along precession axis, no precession takes place. Will the car still feel heavier to turn? I think that the angular momentum cannot be conserved by precessing and if the tyres are made of undeformable rigid material unaffected by the gyro effects, resistance will not be felt. Is it right?

 

[K^2]

It will still seem "heavier" on a turn.