Question: A bead sliding on a rotating parabola
Sunday, 9 of December , 2007 at 9:24 pm
Question: A bead slides along a smooth wire bent in the shape of a parabola, 
. The bead rotates in a circle, of radius 
, when the wire is rotating about its vertical symmetry axis with angular velocity 
. Find the constant c.
Question: A bead slides along a smooth wire bent in the shape of a parabola, . The bead rotates in a circle, of radius , when the wire is rotating about its vertical symmetry axis with angular velocity . Find the constant c.
Category: Classical Mechanics, Questions
Comment by rod
Made Monday, 10 of December , 2007 at 5:04 pm
After some quick and clumsy derivation, I got to:
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.