How Do Gyroscopic Forces Affect Flywheel Torques?

[doodaa]

Hi there,

I need to calculate bending torques on a rotating flywheel. Not sure how to do this. Anyone who can help?

I have a disc with radius r and mass m rotating with omega_z. This means that the moment of inertia is m*r^2/4 for x and y-axis and m*r^2/2 for z axis. (Z-axis is the "natural" center axis of the disc).

If I rotate the spinning disc around the x-axis (or y-axis) I will feel a torque in the y-axis (or x-axis) due to gyroscopic effects. But how does it relate?

 

[Drakkith]

I'm not very familiar with flywheels. What do you mean by "bending torque"?

 

[doodaa]

Well, flywheel or not. Let's just assume it is a rotating disc. Bending torque is ortoghonal to the rotating torque. For exampel, if you have a front wheel driven car the rotating torque accelerates the car and the bending torque turns the wheel.

 

[Cleonis]

Hi there,
I have a disc with radius r and mass m rotating with omega_z. This means that the moment of inertia is m*r^2/4 for x and y-axis and m*r^2/2 for z axis. (Z-axis is the "natural" center axis of the disc).

If I rotate the spinning disc around the x-axis (or y-axis) I will feel a torque in the y-axis (or x-axis) due to gyroscopic effects. But how does it relate?

A discussion of that relation is presented by professor Walter Lewin in lecture 24 of his classical mechanics series, available as a youtube video:
http://www.youtube.com/watch?v=zLy0IQT8ssk"
At 14 minutes into the lecture the discussion of a spinning disk starts.

Remarkably, only the moment of inertia around the spinning axis figures in the relation you are asking about.


Professor Lewin just presents the formula, deriving the formula is beyond the scope of that lecture.

In case you are curious about a derivation, there is one in an article on my own website: http://www.cleonis.nl/physics/phys256/gyroscope_physics.php"