Do the front tires of a car act like gyroscopes, such that a car could steer on a frictionless surface?
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$\begingroup$ Is there an atmosphere providing air resistance or is this in a vacuum? If there is an atmosphere and drag, then for the car to keep moving beyond its initial magical "push" it would have to have thrust, and if it had functional thrust any gyroscopic action that changed its orientation would allow it to steer ("drift" maybe more accurate). $\endgroup$– Jason CCommented Nov 26, 2014 at 3:43
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6 Answers
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No, a car cannot steer on a frictionless surface. This has little to do with gyroscopic action and more to do with conservation of momentum: to turn, even when conserving its speed, the car needs to accelerate at right angles to its motion, which changes the total momentum of the motion. This change in momentum requires a force which, in normal roads, is ultimately provided by the friction between the tyres and the road. In the absence of friction, the car tyres would skid sideways with respect to their rotation (i.e. along the axis) without being able to influence the car's inertia.
It's important to note that, because of the gyroscopic effect, the car can indeed change the direction it's facing pretty much arbitrarily. The easiest way to accomplish this is to have a big flywheel, with a horizontal axis, inside the car, with a mass that's at least comparable to the car's. If you then try to turn the flywheel's axis within the car, you will instead turn the car around the flywheel, because of conservation of the large amount of angular momentum in the flywheel. (This will also cause a torque on the car about a horizontal axis, but this can be cancelled by the normal force from the surface.) However, even if you manage to turn the car 90° from its direction of motion, it will continue to move in the same direction as before, with its wheels skidding perpendicularly across the ice.
Also, as other answers have mentioned, if the car can interact with the air in any meaningful fashion - either by its air intake and exhaust, or by using its bulge as a sail, or by propping up an actual sail - then it will indeed be susceptible to external forces and it will be able to change its direction of motion. Similarly, the car would be able to steer if it could chuck rocks, bump off of other cars, or use rocket thrusters. I don't think this directly answers the core of the question, though.
answered Nov 24, 2014 at 16:48
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2$\begingroup$ @Discipol internal weight shifting alone can't generate net force. You wouldn't be able to change the trajectory with respect to the frictionless plane. $\endgroup$ Commented Nov 25, 2014 at 8:51
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27$\begingroup$ You could perhaps use a gyro to rotate the car, but you'd still end up with a car going in the same direction as before. Just sideways. $\endgroup$– SobriqueCommented Nov 25, 2014 at 13:25
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3$\begingroup$ You could with rocket propulsion. $\endgroup$– gerritCommented Nov 25, 2014 at 15:59
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1$\begingroup$ @supercat but from a distance the car would still be going in a straight line (if you plotted the CoM over time) $\endgroup$ Commented Nov 26, 2014 at 10:16
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1$\begingroup$ You also could with a big fan like a hovercraft. $\endgroup$ Commented Nov 26, 2014 at 13:01
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If the wheels had spun fast enough for a gyroscopic effect to become noticeable, the only result on a frictionless surface (which would be the same without a surface at all) is that when you turn the wheels, the rest of the car would rotate instead of just the front wheels :)
You need some reaction force to alter the trajectory, like a sail or surface friction or thruster.
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13$\begingroup$ Worth noting that the rear wheels would work as gyroscopes resisting whatever motion the "front gyroscopes" would try to impose... But yes, you can change direction in which the car is pointing but that would not provide the lateral force needed to, say, "turn a corner". $\endgroup$– FlorisCommented Nov 24, 2014 at 17:25
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Yes you can
It is actually possible with a real car, but you would have to be very patient to steer a little bit.
Suppose you have built a car with power on the big front wheels to induce a gyroscopic effect. If you rotate the wheels, the direction in which the center of mass is going will not change directly, but the angle in which the rest of the body points will change.
Now we use another property of cars: Often they do their air intake in the front, and have the exhaust in the back. This results in a net force that is roughly pointed towards the nose of the car. So, as you can turn the car a bit by turning the wheels, you change the direction of this force, and will eventually be able to move the car a bit left or right.
answered Nov 25, 2014 at 10:24
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4$\begingroup$ Adding to this; if there is air, the aerodynamics of the car would also help steer it when the body changed direction; especially if it had e.g. a fin on it. $\endgroup$– Jason CCommented Nov 26, 2014 at 3:39
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$\begingroup$ It should also be noted that if you turn the wheels to the left, the car would turn to the right, so steering would be reversed. $\endgroup$– EphCommented Nov 26, 2014 at 15:56
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$\begingroup$ If it was truly frictionless, you wouldn't be able to change the center of mass of the car without an external force. You could definitely change its orientation, but unless it had sails, it will still head in the same direction. $\endgroup$– JasonCommented Nov 26, 2014 at 18:32
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3$\begingroup$ @Jason You should have read the last paragraph too. Dennis points out that there is a tiny amount of air that travels through the car. Now, if the car is in a diagonal orientation (by means of the supposed gyroscopic gyrations), that air will exert a force vector on the internal car body, the angle of which will minutely diverge from the that of its forward momentum. In other words, the cavities inside the car itself function as an (extremely inefficient) sail. $\endgroup$– WillCommented Nov 26, 2014 at 22:46
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$\begingroup$ Vehicle exhaust as thrusters? What a marvelous concept. $\endgroup$– SobriqueCommented Nov 27, 2014 at 13:54
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Since there is no friction, then it will not affect any other forces that may act on the car.
The direction of wind blowing on the car may change its trajectory, as any driver will attest when driving in high winds. Turning the car wheels may have a slight affect on the resultant direction of the force.
If the car has curved roof, then it may acts as wing. Getting the car onto two wheels (ie. by hitting a rock on the road) allows you to change the direction of lift, and you could steer the car in a similar manner to how you steer a plane.
If you opened the car window, and threw something out (or shot a gun), then Newton's third law would move the car in the opposite direction.
The exhaust pipe acts as a jet rocket. If you attach a hose, you could point it in different directions and steer the car this way.
If you stuck a sail on the roof, you could control it by wire with the wheels, and steer like you would a boat.
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$\begingroup$ 3. and 4. will still work even if you neglect air resistance. 5. is essentially the principle behind ice yachts. $\endgroup$ Commented Nov 25, 2014 at 8:58
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2$\begingroup$ Don't sails require some resistance to allow 'steering'? E.g. runners on an ice yacht, hull/water interaction on a boat? Otherwise you'll just be going whatever way the wind is? $\endgroup$– SobriqueCommented Nov 25, 2014 at 13:27
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$\begingroup$ That makes sense, unless the sail acts as a wing, and the vehicle behaves as a plane? $\endgroup$ Commented Nov 25, 2014 at 13:43
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Friction is the only force that would cause the car to move along a different path. On a frictionless surface, the gyroscopic effect could change the orientation of the car a bit, but not the trajectory of the car. In other words, the front car would no longer point along the direction of travel, but would "skid". (That is, if you could call frictionless sideways movement "skidding.")
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On a completely frictionless floor, with the absence of other external forces, the centre of mass of the car will continue in the same trajectory for ever. Hence no steering is possible.
However, irrespective of whether the front wheels are rotating or not, turning of the front wheels will produce a counter torque changing the orientation of the car, albeit by a very small amount. The changes in the orientation of the car and the tyres will be in inverse ratio of MOI(moment of inertia) of the car and the tyres around the wheel steering axis.
Regarding the gyroscopic effect, since the wheels are rotating around an axis parallel to the ground and the turning of the wheels is done around an axis perpendicular to the ground the gyroscopic effect will be experienced around an axis perpendicular to both of these. This axis would also be parallel to the ground. Hence assuming the gyroscopic effect is small owing to the small angular momentum of the wheels, the only effect would be redistribution of the weight of the car over its different wheels. If the front wheels were rotating sufficiently fast the gyroscopic effect would produce enough torque to topple the car over to one side.
