What is the math of this effect?

[baconwitch]

On http://www.gyroscopes.org/1974lecture.asp during segment 8 (from 2:18) an experiment with a gyroscope is conducted.

This is the clip of just that experiment

The gyroscope apparently has less mass. Where can I find math to describe this effect? What is this effect called formally?

Additionally, if this gyroscope were additionally orbiting in a circle with axis parallel to the gyro's axis of rotation, how would the effective centrifugal force of the gyro be calculated?

 

[berkeman]

Very cool experiment! I'd be interested in the math as well.

 

[baconwitch]

Okay after a lot more searching I found this thread...

https://www.physicsforums.com/archive/index.php/t-197183.html

which seems to answer my question.

 

[BruceW]

There's 3 different ways of doing the maths that I know of:
1) use the rules of torque, angular momentum, etc
2) simply calculate what happens in a spherical coordinate system (there will be real forces and fictitious forces)
3) use euler-lagrange equations

2 and 3 are effectively the same thing, but 3 is probably easier. 1 comes from 2 and 3.

 

[pmacias]

The effect described in the video is known as precession, which is the change in the orientation of an object's rotational axis when a torque is applied to it. In this case, the torque is created by the weight of the hanging mass pulling on the gyroscope's axis of rotation.

The math behind this effect can be described using the principles of rotational dynamics and angular momentum. The equation for precession is given by τ = Iω sin(θ), where τ is the torque, I is the moment of inertia, ω is the angular velocity, and θ is the angle between the torque and the angular momentum vector.

To calculate the effective centrifugal force of the gyroscope if it were also orbiting in a circle, we would use the equation F = mω^2r, where m is the mass of the gyroscope, ω is the angular velocity, and r is the radius of the orbit. This equation describes the centrifugal force experienced by an object in circular motion.

In summary, the effect seen in the video is called precession and can be described using equations from rotational dynamics. The effective centrifugal force of the gyroscope in an orbit can be calculated using the equation for centrifugal force.