Bead in a Rotating Hoop, Part 1- Deriving Equations of Motion

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► Dr. Shane Ross, Virginia Tech professor (Caltech PhD)

► Course lecture notes (PDF)

► Chapters
0:00 Introduction of bead in rotating hoop
0:30 Deriving the bead's equations of motion using Newton's laws
1:33 Motion only along the hoop
1:55 Centripetal force
2:25 Modeling friction of bead in hoop
3:30 Tangential direction equation (for theta 𝜃)

► Courses and Playlists by Dr. Ross

📚Attitude Dynamics and Control

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📚Hamiltonian Dynamics

📚Three-Body Problem Orbital Mechanics

📚Lagrangian and 3D Rigid Body Dynamics

📚Center Manifolds, Normal Forms, and Bifurcations

► References:
Steven Strogatz, "Nonlinear Dynamics and Chaos", Chapter 3: Bifurcations

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[malachidrew]

Why does the friction force use angular velocity (theta-dot) rather than linear velocity (r* theta-dot)?

[TriThom]

If we were to do this using the Lagrangian framework, we would need to write equations for T and V. For T, why is there no I*phidot^2 term where phidot is the angular velocity wrt the vertical axis that the hoop rotates around?

[knightace]

I’m isn’t centripetal force radially inward, not outward?

[davidmikota]

Why do we not need to consider the forces in r hat direction? If we did wouldn't we have two equations of motions?