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Question:
Please, please, please, can anyone explain how a gyroscope works? Honestly, thoroughly? Mathematic vector-equation, left- and right-hand rules aside - why does a gyroscope stand up, and why do not really fast ones overcome gravity?



Replies:
If you push sideways a speeding car you do not expect the path of the car to suddenly change so as to lie along the direction of the push. Rather, you expect the car to acquire a little extra velocity in the direction of the push, and the combined action of this new velocity and the car's original velocity to result in a path *mostly along the original direction* but deflected slightly towards the direction of the push. The key insight is that a force changes directly the *velocity* of an object and not its path, and the path only changes eventually, via the change in velocity.

For a mass initially above the ground the force of gravity causes a new downward velocity to build up. If the original velocity of the mass is small, the resulting velocity is mostly the new velocity, and the path of the object is pretty much along the force, i.e. straight down. But if the original velocity is large the resulting velocity can be in a different direction from the force of gravity, and the path will not be straight down. Consider the path of a hit baseball or an orbiting satellite.

Now consider a spinning gyroscope that tilts over slightly. The forces due to gravity and the pressure of the ground on the axle act in the direction of further tilt, that is they add a little downward velocity to mass on the lowered side of the rotor and a little upward velocity to mass on the raised side. The resulting velocities are still mostly in the original direction, around the axle. But due to the new velocities the lowest point on the rotor ends up, a short time later, a little lower than it would originally have been, and the highest point ends up a little higher, and so on. Since the lowest point was headed up and around, that means it heads around, but not up. Similarly the highest point heads around, but not down. The net result is that the circle the rotor traces out rotates around the axle, i.e. the axle tilts perpendicularly to the direction of its initial tilt. Thus the gyroscope precesses, and does not fall down.

For more details and a picture see "An Introduction to Mechanics," Kleppner & Kolenkow, (McGraw-Hill), e.g. page 299 of the 1st edition.

christopher grayce


Simple answer: conservation of angular momentum. In physics there are a few strict conservation laws, and they are very powerful concepts. Conservation of angular momentum is one of them. Once a gyroscope is spinning, it has angular momentum, which is a vector with both direction and magnitude. The direction of the angular momentum vector will not change unless a net torque is applied to the system. An isolated gyroscope has no choice but to "stand up," if it wants to exist in our universe.

Of course in the real world of real physical gyroscopes there are always things like friction in the bearings that will slow down the rate of spin and therefore change its angular momentum.

Simple answer: conservation of angular momentum. In physics there are a few strict conservation laws, and they are very powerful concepts. Conservation of angular momentum is one of them. Once a gyroscope is spinning, it has angular momentum, which is a vector with both direction and magnitude. The direction of the angular momentum vector will not change unless a net torque is applied to the system. An isolated gyroscope has no choice but to "stand up," if it wants to exist in our universe. Of course in the real world of real physical gyroscopes there are always things like friction in the bearings that will slow down the rate of spin and therefore change its angular momentum.

richard a gerber



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