How Does Frictionless Surface Affect Gyroscope Precession?

[MathematicalPhysicist]

1)i have this problem, we have a toy gyroscope, which its pricnipal moments of inertia are known, spins around its axis of symmetry with angular velocity w, and it's tilt with angle a from the vertical on a smooth table (i.e frictionless table). i need to find the precession frequency?
im given a hint that i need to think about what has changed from the typical gyroscope problem.

i don't see what has changed here.

2) i have another question, i need to find the velocity of precession without any appriximation of the gyroscope, i need to find what is the condition for the precession.
in class we made the approximation theat the angular velocity around the body axis is much more bigger than the velocity of precession, and we have neglected the angluar momentum that is gained by the precession.
so how would i calculate it, obviously the gain by the precession i should divide it to tangential and parallel components, but I am not sure what is L_p the angular momentum of the precession.

your help is appreciated.

 

[BobG]

What's the typical gyro problem in your book?

To find the precession rate, divide the torque applied to the system due to gravity by angular momentum of the gyro. For torque, if the gyro's at an angle, remember you need the horizontal distance that the top of the gyro is displaced instead of the length of the gyro (i.e. - you need the lever arm).

Technically, this gives you the tangent of the angular velocity of precession, but you usually have such a small angle that the tangent is equal to the angle.

http://hyperphysics.phy-astr.gsu.edu/hbase/rotv2.html

 

[MathematicalPhysicist]

yes, i think i solved question two, but about question two, what is the condition that needs to be met in order that precession will occur?

 

[BobG]

An external torque. The only way to change your angular momentum vector is with an external force. The precession stops as soon as the torque is removed. (Of course, it's kind of hard to stop applying gravitational torque. The conditions are more relevant for things like spacecraft stabilization where you have to deal with torques from thruster firings and so on.)

As opposed to nutation, which can occur because heat dissipation, etc, and changes the rotational kinetic energy without changing the angular momentum.