Recent content by trytodoit

The no horizontal force seems auto satisfied, which cannot introduce a equation into the system.

Today, I discussed my friend about two rigid beams impact and assuming no energy loss in the impaction. As in the above figure, the upper beam move down with a uniform velocity ##v_c##, and hit a beam with ##0## velocity. After that the above beam will rotate and move away, which can be...

In my opinion, you cannot define the shortest path by tight the string. For the sphere, it happens to be only two stable states, as mentioned by @micromass, but generally you still cannot say a stable state of the tight string is the shortest path for all kinds of shapes. Even worse, according...

Woo, it looks quite hard to proof this statement.

Yes, therefore the proofs assuming uniqueness of the shortest path are not that intuitive as it sounds. Any better proof for this simple statement.

There are plenty of proofs for the statement, but I do not find one which is not rely on other assumptions. Here are some common proofs of this statement: https://en.m.wikipedia.org/wiki/Great_Circle#Derivation_of_shortest_paths This proof require the path to be differentiable, which is not a...

@https://www.physicsforums.com/threads/how-to-derive-the-formula-for-moment-of-inertia-of-polygon.809203/members/steamking.301881/ Thanks for your hint! I worked it out.

Sorry to bring this question up again. @aridno provides a nice formula of the moment of inertia I about the centroid in https://www.physicsforums.com/threads/calculating-polygon-inertia.25293/ as: $$...