Undergrad Gravitational Illusions -- Two balls rolling down differently-shaped ramps

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The discussion centers on the concept of gravitational illusions, specifically how two balls roll down differently-shaped ramps. Participants emphasize the importance of hands-on problem-solving to truly understand the physics involved, rather than relying solely on mathematical proofs. The Brachistochrone curve is mentioned as a relevant mathematical solution to the problem of determining which ball reaches the bottom first. Contributors are encouraged to share their own mathematical solutions for feedback and discussion. Engaging with the problem directly is highlighted as essential for deeper learning.
Jurgen M
Without this test,using only math, would you prove that left ball will comes first?

 
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Why make us do all the work? You'll never learn unless you do the problems yourself.

Write your own mathematical solution and post it here. We'll comment on it.
 

Thread 'Reference frames, center of rotation, etc'

Topic about reference frames, center of rotation, postion of origin etc Comoving ref. frame is frame that is attached to moving object, does that mean, in that frame translation and rotation of object is zero, because origin and axes(x,y,z) are fixed to object? Is it same if you place origin of frame at object center of mass or at object tail? What type of comoving frame exist? What is lab frame? If we talk about center of rotation do we always need to specified from what frame we observe?
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