The center of a long frictionless rod, pivoted at the origin, is forced to rotate at a constant angular velocity Ω in the horizontal xy-plane. Write down the equation of motion for a bead threaded on the rod, using the coordinates x and y where x is measured along the rod and y perpendicular to it. Solve for x(t). What is the role of the centrifugal and coriolis force?
Newton's Second Law in a rotating frame?
The Attempt at a Solution
Since the bead's fixed to move along the wire, I've eliminated the equation for the motion along the y-axis. The bead's position along the x-axis varies with time, and based on the coriolis effect, the bead should slide out away from the origin.
I'm not sure how to deal with the math from here though. Any tips on how to get started would be greatly appreciated.