Gyroscope precession - WHY? (What's the cause?)

[panathi]

«(...) a torque τ applied perpendicular to the axis of rotation, and therefore perpendicular to L, results in a motion perpendicular to both τ and L. This motion is called precession.»(http://en.wikipedia.org/wiki/Gyroscope)



Why does this happen? Assumpting this makes all further calculus very easy and we can calculate the angular speed of the precession motion without difficulty (see http://physics.nad.ru/Physics/English/gyro_txt.htm).

But WHY do we assumpt this? What's the reason why the gyroscope does not rotate over the "expected" axle, as it does when the rotor is stopped? (I do not want you to tell me about experimental facts... I think it is pretty obvious that I am seeking for a theoretical explanation)


Please answer me as soon as possible. Thanks in advance.


Stay cool!

 

[pervect]

«(...) a torque τ applied perpendicular to the axis of rotation, and therefore perpendicular to L, results in a motion perpendicular to both τ and L. This motion is called precession.»(http://en.wikipedia.org/wiki/Gyroscope)
Why does this happen?

Because the angular momentum of the gyroscope is conserved.

Draw the vector L for the initial angular momentum of the gyroscope.

Draw the vector \Delta T \tau for the amount of angular momentum transferred to the gyroscope from a torque \tau acting for a time \Delta T.

Observe that the final angular momentum of the gyroscope is given by the intial angular momentum plus torque*time.

 

[Tide]

First, it is not an assumption! It follows quite rigorously from Newton's Laws of Motion applied to a rotating system or rigid body. As for the "expected" behavior, it is only "expected" if you insist on thinking about it as a nonrotating system.

You can find an adequately detailed explanation here: http://en.wikipedia.org/wiki/Precession

 

[jtbell]

It follows quite rigorously from Newton's Laws of Motion applied to a rotating system or rigid body.

This is easier if you analyze a simple hypothetical object such as two equal point masses attached to the ends of a massless rigid rod, that rotates around the midpoint of the rod. A long time ago, I saw a derivation that used this model, but I don't remember where.

 

[panathi]

Thank you guys :)

«The permanent axis must turn towards this line, since the body cannot continue to rotate about any line which is not a principal axis of maximum moment of inertia; that is, the permanent axis turns in a direction at right angles to that in which the torque might be expected to turn it.»

(http://en.wikipedia.org/wiki/Precession)

This piece of information clears my doubts and explains why the gyroscope makes de precession motion. But why does the body tend to rotate around a line which is a principal axis of maximum moment of inertia?

Thank you all that answered me promptly. :)


Farewell

 

[SockCymbal]

http://www.thehowandwhy.com/Gyroscopic.html

 

[panathi]

a principal axis of maximum moment of inertia

How do you define this?

 

[SockCymbal]

How do you define this?

Its pretty self explanatory. Its simply the axis that yeilds the highest (most resistivity to spin) moment of inertia.

The MINIMUM moment of inertia about any axis passes through the centriod (center of mass of a uniformly dense object).

 

[panathi]

since the body cannot continue to rotate about any line which is not a principal axis of maximum moment of inertia

Can the axis who passes through the centriod be considered the principal axis of maximum moment of inertia? This makes no sense for me. :s Please keep helping please.