Recent content by wrobel

I fed my English translation of this problem (from the initial post) to an AI. It correctly recognized it as problem number 2.1.51 from Savchenko, but then provided an incorrect solution and the wrong answer. Some people, to put it mildly, somewhat overestimate the omnipotence of this thing I guess.

????? By definition, purely translational motion is when all the points of a rigid body move with the same velocity

My version is $$L=mr^2\dot\theta^2(1+\cos\alpha)+mgr\theta\sin\alpha$$ hopefully that is the same:)

A slab rests on two massless rollers of different radii such that the angle of the slab's inclination is ##\alpha##. There is no slipping between the slab and the rollers, nor between the rollers and the ground. Prove that the slab moves with purely translational motion and find its...

Any set can be covered by a finite intersection of closed sets; simply take its closure. Furthermore, the closure of a set is itself the intersection of all closed sets containing it.

mech problems I like 3D problems more, but these are also great

Almost always, the field of scalars is the field of real or complex numbers.

The book is pointless. The author yanked random bits from differential geometry, linear algebra, calculus, and physics. It’s the best way to make sure the reader ends up understanding absolutely nothing.

"No forces" and "zero net force" are in fact the same thing, since we are considering a single particle. If you have a particle at rest in an inertial frame, you can not distinguish one case from another

Do that. will see how GPT deals with it

Read decent books: Finite-Dimensional Vector Spaces by Paul R. Halmos

Write the angular momentum change theorem about the suspension point of the chain; ##(r>0)##

At the point where the circle is tangent to the straight line, the acceleration of the chain links undergoes a discontinuity. Just a remark

Why, for example, is it a semicircle? There are plenty of other curves out there.

-