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.

 

[PJC01]

I cannot provide a definitive answer without conducting experiments or simulations to accurately determine the behavior of the car in these scenarios. However, I can provide some insights and considerations that may help you in your attempt to solve these problems.

Firstly, the gyroscopic effect is a phenomenon where a spinning object (in this case, the flywheel) resists any force applied to it that tries to change its orientation. This is because the spinning object has angular momentum, which is a property of rotating objects that makes them resistant to changes in their rotational motion.

Now, let's consider the first problem. In this scenario, the car is not on a road and is in free space, so there is no external force acting on it except for the jets that are fired from the left-front and right-rear corners. These jets will create a torque that tries to steer the car to the right. However, because the flywheel is spinning clockwise, it will resist this motion and try to maintain its orientation. This will cause the car to precess in the vertical plane, as you have correctly stated.

To determine the minimum angular velocity of the flywheel that is required to prevent the steering motion, we need to consider the balance of torques acting on the car. The torque created by the jets will be counteracted by the torque created by the spinning flywheel. The magnitude of the torque created by the flywheel is given by T = I * w, where I is the moment of inertia of the flywheel and w is its angular velocity. So, to prevent the steering motion, the torque created by the flywheel must be greater than or equal to the torque created by the jets. Therefore, the minimum angular velocity of the flywheel can be calculated as w = t/I, where t is the torque created by the jets.

For the second problem, the car is on a road and is trying to take a right turn. In this scenario, the bearings are strong enough to prevent the flywheel from precessing in the vertical plane. This means that the flywheel will not resist the steering motion and will allow the car to turn. However, the spinning flywheel will still have some effect on the car's stability and handling. This is because the gyroscopic effect will cause the car to resist any changes in its orientation, which can affect the car's stability and handling during the turn.

In conclusion, your answers seem to be on the right track, but it