Lagrangian Example: Sliding Bead on a Rotating Hoop

Photo: Rhett Allain

I don’t know who came up with this problem, but it’s actually pretty fun. Here’s the deal:

• Start with a hoop with a radius of 0.05 meters. It rotates about an a vertical axis (in the y-direction) that passes through the plane of the hoop (see the sketch above).
• The hoop rotates with a constant angular velocity of 10 rad/s.