Classical Mechanics: Cylindrical Coordinates Mass on a Cylinder

This is part of my classical mechanics series. You can find all my videos in the series in the following playlist.

A frictionless particle is confined to the surface of a vertical cylinder of radius R. At time t, the particle is at height h with a velocity in the angular direction (vertical velocity is zero) of w0. Write Newton’s second law in terms of cylindrical coordinates. Determine an equation of motion of the ball.

Python code

[brookestephen]

mapping physical behavior to calculations, using graphical programing, just never get old!

[BradleyG]

Would love a video on the derivation of the acceleration vector formula, with an emphasis on intuitive understanding. I know how to derive it, and I know what most of the terms represent, but I don't entirely understand how they come together to give acceleration.

[KR-jkon]

I believe you are missing mass term in your force calculations - For example, you write N = -R*theta_dot^2. The LHS is a force and the RHS is an acceleration

[Rick_Cavallaro]

A related fun problem... can you roll a ball on the inside of a vertical cylinder in such a manner that it maintains its circular and horizontal path (ignoring frictional losses)?