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"

 

[PJC01]

Sure, I can help with this problem. Gyroscopic forces on a flywheel can be quite complex, but I'll try to break it down for you. First, let's define some terms:

- Gyroscopic forces: These are the forces that act on a rotating object, such as a flywheel, due to its angular momentum.
- Flywheel: This is a rotating disc or wheel used to store kinetic energy.
- Bending torques: These are the forces that cause a rotating object to bend or twist.

Now, to calculate the bending torques on a rotating flywheel, we need to consider the gyroscopic forces acting on it. The moment of inertia, or the resistance of an object to changes in its rotational motion, plays a key role in this calculation. In your case, the moment of inertia for the x and y axes is m*r^2/4, while for the z-axis it is m*r^2/2.

When you rotate the flywheel around the x-axis, you are changing its angular momentum in the y-axis. This creates a gyroscopic force in the y-axis, which produces a bending torque in the x-axis. Similarly, rotating the flywheel around the y-axis will create a gyroscopic force in the x-axis, resulting in a bending torque in the y-axis.

To calculate the magnitude of these bending torques, we can use the equation T = I*alpha, where T is the torque, I is the moment of inertia, and alpha is the angular acceleration. In this case, alpha would be the change in angular velocity caused by the gyroscopic force. So, the greater the angular acceleration, the greater the bending torque on the flywheel will be.

I hope this helps you understand the relationship between gyroscopic forces and bending torques on a rotating flywheel. If you have any further questions, don't hesitate to ask. Good luck with your calculations!