Question: A bead sliding on a rotating parabola

December 9th, 2007

Question: A bead slides along a smooth wire bent in the shape of a parabola, z = cr^2. The bead rotates in a circle, of radius R, when the wire is rotating about its vertical symmetry axis with angular velocity \omega. Find the constant c.

Comment by rod

Made Monday, 10 of December , 2007 at 5:04 pm

After some quick and clumsy derivation, I got to:

c = \frac{\omega^2}{2 g}

Is it right?

Comment by eldila

Made Monday, 10 of December , 2007 at 6:21 pm

yep, you got it.

May I ask, how you came up with the answer. I solved it using Hamiltonian Mechanics.

Also, I will try to get my latex wordpress plugin to work on comments.

Pingback by A bead sliding on a rotating parabola « Reasonable Deviations

Made Tuesday, 11 of December , 2007 at 1:45 am

[...] bead sliding on a rotating parabola Via jkwiens.com, here’s an interesting [...]

Comment by rod.

Made Tuesday, 11 of December , 2007 at 1:52 am

As you can see from the ping above, I wrote a post on my blog, with my clumsy and dull vector-based solution. It would look more elegant using Hamiltonian Mechanics, but sometimes the ugly solution is faster ;-)

Comment by eldila

Made Tuesday, 11 of December , 2007 at 7:11 am

I totally agree with you. The only real benefit of using Hamiltonian Mechanics is that you get a generic differential equation which can solve different variations of the problem.

I was going to play around with maple to see if I could come up with a more general solution. I will see what I come up with.

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