Gyroscopes

[ronthepon]

I feel like I am being mocked.

 

Hey! Rep points do mean a lot for me!

[Jay-qu]

he moved me 4 rep points :eek2:

[Turtle]

I feel like I am being mocked.

 

Hey! Rep points do mean a lot for me!

 

No mocking here Ron. I have to spread some rep around to others before the interface allows me to give to you again. I won't forget.:eek:

Wow Turtle! Taking cover behind that desk was the only thing you did right that time!!!

:hihi: I properly assessed the probable outcome too. That plus the ducking is 2 things right.:hihi:

Now where'd I put those motors...

[TheBigDog]

When I was growing up in Mt View CA we were just down the road from NASA and Aimes Research Center. Used to have an assembly every year where they would demonstrate cool stuff for we wee kids. One demonstration I remember to this day was from a woman astronaught (don't remember her name) who had a kid sit on a chair that could spin while holding a front fork from a bike with a wheel mounted in it. Sshe spun the sheel really fast and then the kid would tip it one way or the other to make the chair spin. It was really cool. That is always my vision of gyroscopes.

 

Bill

[TheBigDog]

he moved me 4 rep points :eek:

Brotherly conduct is like mega-vitamins. Don't worry Ron, Turtle doesn't forget.

 

Bill

[ronthepon]

I feel like I am being mocked.

 

Hey! Rep points do mean a lot for me!

I was just ...um... joking again...

[Qfwfq]

[math]\frac{dL}{dt}= T[/math]

This is the formal reason for the behaviour, including the effect which The BigDog describes. But how does it happen in detail?

 

Imagine a nice bike-wheel rim type distribution of mass. At each point, instant velocity is tangent to the rim. Now suppose you are turning the axis and ask what forces need to be applied. OK, let's suppose the axis horizontal. Forces are necessary due to acceleration of some part of the solid body, times its mass, so work out which bits are accelerating due to the turning axis, and how. The velocity of each bit changes only in direction and the centripetal terms cancel out, this doesn't change by turning the axis. The bits that are at the same height as the axis aren't otherwise accelerating, the vertical velocity doesn't change direction. The highest and lowest bits have horizontal velocities and these do change as the axis turns, this change is horizontal and at right angles to the velocity, equal and opposite for the top and bottom bit and these constitute a pair that with a pure torque. For intermediate bits, the same goes for the horizontal component of velocity and to work it out quantitatively, considering the two bits at each height gives a neat balance. With a bit of trig you can write the integral.

[ronthepon]

Or, you could mention the concept of moment of inertia...

[Racoon]

Turtle doesn't forget.

 

:)

Oh, but he does. Just ask him to explain some of the books he's read. :D

 

I remember quite a few years ago, when Turtle lived in a certain Plex, his construction of a Gyroscope! (among walls of other science do-dads, novelties, and projects )

I was way dumber then, if thats even possible, but I was amazed. ;)

Make no mistake about it.

Turtle knows his stuff! ;)

 

That must've been X many years ago, and the memory is still clear as mud.

Gyroscopes are neat!

[Qfwfq]

Or, you could mention the concept of moment of inertia...

That's simplifying a bit too much.

 

When the gyroscope has no precession and no nutation, you can say that L, angular momentum, is equal to [math]\norm \omega[/math] times the moment of inertia for the gyroscopic axis. Otherwise, you need to consider the elipsoid of inertia and the Poinsot cones, L and [math]\norm \omega[/math] don't have the same direction...

[Turtle]

That's simplifying a bit too much.

 

When the gyroscope has no precession and no nutation, ...

 

Sweet Q! New nutation! I knew of precession, but never heard of the other 'nodding' motion gyroscopes exhibit.

http://en.wikipedia.org/wiki/Nutation

 

;)

[Qfwfq]

Another thing that came to mind: suppose you're confronted by the problem of

":doh: now which of these eggs still have to be boiled and which already are? :confused:"

[Turtle]

Another thing that came to mind: suppose you're confronted by the problem of

":doh: now which of these eggs still have to be boiled and which already are? :confused:"

 

By spinning them of course! The hard-boiled egg is spinning nice, but un-boiled eggs they lurch like dice.:eek_big: