/sci/ - Science & Math

Momentum, dingus.

Nobody?

Angular momentum. Also precession.

I know it's because of momentum, but I don't understand why.

I get that dL/dt = r x F and that the vector it points towards us (in the picture) but I still don't get why that means it won't fall down.

Buump!
Any mathematical proof?

Have you tried maybe looking at it in a simple way?

Imagine a spinning top made of just two weights on a stick, perpendicular to another stick

When it's spinning, the momentum might look like these red vectors.

As tangents, they naturally point away from the circle, constrained by the stick and cancelling eachother's movement out though, they can't move further from the center of the top, so they go the only direction they can go, which is round a circle

Meh this is a child's toy and I don't understand it

Yeah that is a simpler way to look at things but what I don't understand is if we involve gravity here why would those balls not fall to the ground if tilted a little? While they do cancel each other out won't gravity still add to it? Meaning the Fnet (total force) is equal to F - F + G = G? Both of those balls are being pulled to the ground by gravity.

Has spin angular momentum by virtue of its... Spinning. When it leans to the side this produces a torque which moves it back into a steady position, but lowers how much energy it has, so it steadily slows down. As speed gets lower, it has less spin angular momentum, so it can't produce a big enough torque and eventually falls over.

>>4047008
Book - Theorical Mechanics of Particles and Continua by Fetter et all

Chapter 5 - Rigid Bodies

Page 156 - Symmetric Top: Torque Free motion
157 - Equations of Motion and First Integrals

The derivation isn't trivial, you actually need to know a good amount of undergrad physics to do it.

hmm ok let me try...

imagine that the two weights aren't attached by a rigid rod, but by a rope.

Now, if you move the center rod where the ropes attach toward one weight, the other weight is pulled along while the rope between the pole and the other weight loses tension.

Now the weight on the tense rope keeps pulling at the pole, but the other weight won't pull at the pole until the rope has fully extended and is tense again, so until then only one of the weights movement is pulling at the pole, and that is sort of why when you tilt a spinning top, it moves like 90° to the direction you actually tilted, this happens again and again and that is how the top stabilizes despite being tilted.

I understand to the point when torque comes into act. Why does the gravity produce a torque which moves it into steady position? Why is there no torque when there's no spinning?

>>4047269
\thread

>>4047277
How about you actually read the fucking book?>>4047269

\thread

Where to get the book?
:)

Also I hadn't refreshed. As for the rope idea: Why then does it start moving into a certain direction? (clockwise or counter-clockwise depending on which way we spin the two weighs)

>>4047269
Page 161
"Symmetric Top: One fixed point in a gravitational field" is what OP is looking for.

You can look at the book on Google Books

>>4047301
"Google Books" has those chapters (maybe even the whole book) free. >>4047318

Cheers

>>4047301
I was thinking something like this:

>>4047269
>>4047318
>>4047321
/sci/ delivers

>>4047340
>>4047301
>>4047273
Rope idea is "cute", but It seems like shit.
Just read the book, it explains it all and has all the equations.