A bead of mass m slides on a long straight wire which makes an angle alpha with, and rotates with constant angular velocity omega about, the upward vertical. Gravity acts vertically downard.
a)Choose an appropriate generalized coordinate and find the Lagrangian.
b)Write down the explicit Lagrange's equation of motion.
The Attempt at a Solution
I'm a bit confused. They mean only 1 generalized coordinate so this mean the system has only 1 degree of freedom. Ok.
The center of my coordinate system is the point where the wire and the vertical meet. I call x the distance from this point to the mass. This means [itex]V=mgx \cos \alpha[/itex].
I'm having a hard time in finding the velocity of the mass. Not only it has a circular motion with tangential speed [itex]\omega x \sin \alpha[/itex] but can also move along the wire with velocity... [itex]\dot x[/itex]? Adding up these 2 speeds and squaring them in order to get the kinetic energy would not match the given answer.
I'd like some help to get the kinetic energy of this particle/mass. Thank you.