Unstable Equilibrium: Hyperbolic Solutions for High Speed Rotating Pendulums скачать в хорошем качестве

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 How do we actually SOLVE physics problems? What to think about? What symmetry can we see and what math could be used? These are important questions in physics education. We need to learn the laws of physics and how to apply them. Let me break down the exact thought process to enable your goal of becoming a top student! Subscribe/Like for weekly demonstrations of problem solving techniques. 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 #physicsquestions #physicsproblems #physicsexplained #apphysics #jeephysics #IPhO #physicsolympiad #newtonslaw #classicalmechanics