Bead on straight wire that rotates around origin

[msimmons]

Question:
A Particle of mass m can slide freely along a straight wire placed in the x-y plane whose perpendicular distance to the origin O is h. Denote the projection of O on the wire by on the wire by C. The line OC rotates around the origin (in the x-y plane) at a constant angular velocity $$\omega$$. The particle is subject to a gravitational force acting down the y axis. Find the equation of motion.

I'm having a bit of trouble figuring out how to set up the Lagrangian. Can anyone perhaps give some insight on a way to think about the problem that could lead to the Lagrangian?

 

[gabbagabbahey]

Question:
A Particle of mass m can slide freely along a straight wire placed in the x-y plane whose perpendicular distance to the origin O is h. Denote the projection of O on the wire by on the wire by C. The line OC rotates around the origin (in the x-y plane) at a constant angular velocity $$\omega$$. The particle is subject to a gravitational force acting down the y axis. Find the equation of motion.

I'm having a bit of trouble figuring out how to set up the Lagrangian. Can anyone perhaps give some insight on a way to think about the problem that could lead to the Lagrangian?

Well, for starters, this is a 2D problem with rotation about the origin, so you'll probably want to use polar coordinates. What is the kinetic energy of a point mass in polar coordinates? Is the wire's mass negligable? (If not, it will have some kinetic energy as well) What (external) forces are the particle and wire subject to? What is the potential that gives rise to that force (or forces)? What constraint(s) are placed on the mass and wire?

 

[msimmons]

Huh. Polar coordinates help out a bit.

That was all I needed to get it right. Oops.

Thanks!