1. The problem statement, all variables and given/known data We have a bead sliding on a frictionless hoop oriented vertically. First the hoop rotates about its center with rotation axis perpendicular to its plane. Second, the hoop rotates about a vertical axis as well. In both of these cases, are the constraints holonomic or nonholonomic? Are the time dependent or independent? 2. Relevant equations 3. The attempt at a solution In both cases the constraints are time dependent because they depend on the rotational velocity. In the first case, it is holonomic - you can define the bead's position in terms of time and the generalized coordinates. However, I'm not sure about the second case. I think it might be holonomic as well, because we should be able to describe its constraints knowing only the hoop's equations of motion. The hoop has 2 degrees of freedom, theta and phi, and we define an origin we should be able to describe the particle's location at any time using just theta and phi. Am I correct in my argument that the constraints in both cases are holonomic? This question has my confidence completely stumped!