Unstable Equilibrium: Hyperbolic Solutions for High Speed Rotating Pendulums

Dive into the fascinating world of classical mechanics with this deep dive into a pendulum mounted on a rotating platform! We'll explore how constant angular velocity $\Omega$ affects the pendulum's motion, from stable small-amplitude oscillations to wild instability when centrifugal forces overpower gravity.

In this video you will learn things not even your professor knew!

Let me know in the comments which problem you want me to solve next?

0:00 – Intro
2:39 - Gravity and centrifugal force: phi-direction
7:16 - Newton's law in phi-direction
9:02 - Harmonic solution for small phi
10:09 - What about a fast platform rotation?
12:11 - Hyperbolic solution for small phi
14:36 - Trap: Hyperbolic solution invalid for large phi
15:30 - Numerical exact solution
16:21 - Oscillatory exact solution: large angles
17:50 - Find the potential energy U!
21:22 - Find the mechanical energy E
22:11 - d phi /dt =0 in the numerical solution is analyzed

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Keywords: Pendulum, RotatingFrame, Instability, Oscillations, CentrifugalForce, NonInertialFrames, RotationalDynamics, Efficient problem solving, JEE Advanced physics, Physics Olympiad, classical mechanics, center of mass, JEE mechanics, AP Physics C, beautiful physics solution

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