Gyroscope equations

[Corey White]

Gyroscopes are well-known for their ability to maintain stability and resist
changes in orientation. Their behavior is governed by precession, a
principle that describes how a spinning object responds to external forces.


If you drop a spinning gyroscope alongside a regular object, the gyroscope
will not simply fall straight down. It will follow a slower spiraling
path and land after the other object.

To test this idea, imagine a heavy wheel mounted on an axle, spinning
rapidly in a vertical plane. If you rotate the axle in a horizontal plane
while the wheel is still spinning, the wheel will either float upward or
sink downward, depending on the direction of rotation. This is a 90 degree
movement up or down.

We can describe this with math.

d is the diameter of the wheel.
L is the length of the axle

We calculate the total distance traveled by a point on the wheel as it
rotates once, while the wheel spins around the axle once.

The axle describes a circular path of radius L, and the wheel describes a
circular path of radius d/2.The distance traveled is the sum of these two
circular paths.

D1=π * d * sqrt(2)+2π * L

This equation combines the motion of both the wheel and the axle. The 2π*L
term represents the circumference of the circular path made by the axle

If the wheel also moves 90 degrees vertically during the rotation, then we
also add the vertical movement, which is simply the length of the axle, L,
because the wheel moves up by half its diameter in the vertical direction.
(or down)

D2=π * d * sqrt(2)+2π*L+L

Here, 2π*L represents the circular motion of the axle, and L represents the
vertical distance the wheel moves during the rotation.

You can watch the experiment here:

The question is where the additional energy comes from to move L 90 degrees.

[David Dalton]

Post by Corey White
Gyroscopes are well-known for their ability to maintain stability and resist
changes in orientation. Their behavior is governed by precession, a
principle that describes how a spinning object responds to external forces.
If you drop a spinning gyroscope alongside a regular object, the gyroscope
will not simply fall straight down. It will follow a slower spiraling
path and land after the other object.
To test this idea, imagine a heavy wheel mounted on an axle, spinning
rapidly in a vertical plane. If you rotate the axle in a horizontal plane
while the wheel is still spinning, the wheel will either float upward or
sink downward, depending on the direction of rotation. This is a 90 degree
movement up or down.
We can describe this with math.
d is the diameter of the wheel.
L is the length of the axle
We calculate the total distance traveled by a point on the wheel as it
rotates once, while the wheel spins around the axle once.
The axle describes a circular path of radius L, and the wheel describes a
circular path of radius d/2.The distance traveled is the sum of these two
circular paths.
D1=π * d * sqrt(2)+2π * L
This equation combines the motion of both the wheel and the axle. The 2π*L
term represents the circumference of the circular path made by the axle
If the wheel also moves 90 degrees vertically during the rotation, then we
also add the vertical movement, which is simply the length of the axle, L,
because the wheel moves up by half its diameter in the vertical direction.
(or down)
D2=π * d * sqrt(2)+2π*L+L
Here, 2π*L represents the circular motion of the axle, and L represents the
vertical distance the wheel moves during the rotation.
http://youtu.be/GeyDf4ooPdo
The question is where the additional energy comes from to move L 90 degrees.

You might gets some informed feedback from the
moderated group sci.physics.research .

But I have saved your posts and will have a closer
look myself later.