Loxias
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Homework Statement
A bead of mass m slips without friction an a vertically oriented hoop of radius R.
The hoop rotates around the z axis at a constant rate w.
(question 4 if anyone wants to see the figure)
http://phstudy.technion.ac.il/~wn114101/hw/wn2010_hw05.pdf"
Homework Equations
Write the Lagrangian for the system
The Attempt at a Solution
I need to transform coordinates.
I thought about transforming to spherical ones.
constraints : r = R, \phi = wt
x = R sin(\theta) cos(wt), y = R sin(\theta) sin(wt) , z = R cos(\theta)
does this seem right? because when I try to write the velocity I get a very ugly equation
\dot{x}^2 + \dot{y}^2 + \dot{z}^2 = \dot{\theta}^2R^2 + w^2R^2sin^2(\theta) - 2\dot{\theta}wR^2 sin(\theta)sin(wt)cos(wt)cos(\theta) +2\dot{\theta}wR^2cos(\theta)sin(wt)sin(\theta)cos(wt) + \dot{\theta}R^2sin^2(\theta)
which simply doesn't look right..
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