When Will The Ball Fall? | Classical Mechanics

In this video, I demonstrate a way of using Lagrange multipliers to solve for when a ball looses contact with a circle that it's rolling off of. This technique could be applied to other cases where a constraint applies for only some of the time evolution of a system, and it is necessary to calculate the point where it stops applying.

Typo at 2:25: On the RHS of the first equation of motion, there should be a square on the theta-dot.

[nr]

After doing all that quantum shit, analytical mechanics is still so beautiful.

[williamperez-hernandez]

2:25 The first equation of motion has a typo error. The first term in the RHS should be ma (theta dot)squared.
Don't think the title is appropiate. This solution is for a non-rotating object, say a flat brick. If we assume the ball rolls without slipping on the hemisphere surface, the problem is much complicated. Likely will depend if the ball is a solid sphere (like a baseball) or a spherical shell (like a tennis ball).

[chilling]

This is kind of an overkill...can be easily solved using simple circular motion