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Operation of a Gyroscope
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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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Update: June 2012
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