1. Aug 17, 2011

### Shivanand

Consider the case of a common demonstration which you would find in videos. A bicycle wheel mounted on a shaft is set into rotation, axis is made horizontal and the shaft stays horizontal for sometime and eventually goes down as the wheel spin slows down due to friction.

My questions are

1) What torque balances the gravitational torque vertically and the precession torque horizontally (applying Newton's second law) ?

2) Let the torque resisting the vertical fall of shaft be R and torque due to gravity be T. Since the shaft finally tilts down is R more than T and why does this happen?

3) How is the resisting torque (against gravity) R dependent on
a)Rate of spin
b)Gravitational torque T ?

2. Aug 18, 2011

### Bill_K

Shivanand, This question shows that you have a bit of misunderstanding with the concepts. Let's see if we can clear it up. Here's some questions for you:
a) What is the general relationship between torque and angular momentum?
b) There is a torque on the gyroscope caused by the downward force of gravity and the upward reaction force of the support. In what direction does this torque point?
c) What is the angular momentum of the spinning gyroscope? In which direction does it point?
d) Is the angular momentum constant? Remember it is a vector.

Also you mentioned Newton's Second Law. Does Newton's Second Law apply to torques or to forces?

3. Aug 18, 2011

### IttyBittyBit

No, even if the shaft continued rotating at the same speed (for example, if it were motorized) it would still slowly be pulled down.

4. Aug 18, 2011

### DaveC426913

It is against the rules for PF members to provide you with answers. You must show your attempts at the solutions before we can help you.

5. Aug 23, 2011

### Shivanand

Hi,

Sorry for the late reply. I tried hard to understand and I thought I need help from people like you. I attempted to get a solution but I am too confused. Please excuse me for asking straight away and not posting my attempts in this thread

I will make my questions simple. If I could get an explanation, I would be able to understand. Please bear with me if my questions were/are annoying and if I seem like a noob. I am still learning.

1) Does a spinning bicycle wheel supported at one end of its shaft fall down if the rate of spin of the wheel (angular velocity) is constant?

2) If it does not fall down, is there a critical angular velocity above which the shaft does not fall? Or do the wheel and shaft fall irrespective of angular velocity (high or low) of the wheel?

It was my mistake to have told Newton instead of Euler. I meant Euler's equations. Sorry for that

Last edited: Aug 23, 2011
6. Aug 24, 2011

### Quinzio

It depends. But not on the spinning speed. Someone before gave you the answer. It is important you understand why to master properly the gyro behavior.

It can always fall down, without anything you can do against it by adjusting the angular speed.
Try to understand why (it's not so easy), then eventually come back.

7. Aug 24, 2011