There are a few things in your response that I would like to comment on, but first, let me preface that in my video, I am not justifying a position where professors provide no solutions for practice problems. I always provide multiple practice exams, but only solutions for a select number of those practice exams, so that enables students with various learning needs to study those solutions and learn some things from it. I do provide solutions for some questions, just not all as this promotes simply studying/memorizing past solutions. The remark that concerns me in your response is that you state "...a third of [lecture content] which has never come up in an exam nor ever will is completely off topic." This comment makes it seem that you feel the goal of a course is to pass an exam. This is the wrong perspective. All things taught in a course lecture should be relevant to the deep understanding of the content that is being strived for in the learning objectives of the course. Thus studying it is in line with the learning objectives of the course and is a worthwhile endevour. Thus, what you are identifying as being completely off topic is likely connected to the deep understanding that is necessary to apply the concepts to new problems.

You are correct. I wasn’t attempting to show an accurate number of orbits with the illustration, only illustrate that there is a wobble.

I am certainly not afraid of AI replacing humans. But I think a lot of the fear of AI in education hinges around the fact that education will have to evolve to properly include/leverage AI as a tool, but there is resistance to this as t will require a lot of time and effort. Particulalry in the area of assessment where we rely on assignments with well defined and expected answers (the type of thing AI tends to be good at finding).

Very insightful interview. The answers of ChatGPT are uncannily similar in realism to those of the robot R. Daneel Olivaw. Also in their honesty on limitations and origin. Hopefully, the Asimov laws were implemented as well in ChatGPT.

It’s not that there is excess kinetic energy, but that more kinetic energy is needed for the same movement. So in the experiment, both objects had the same potential energy, and that potential energy is converted to kinetic energy, but due to the distribution of mass in the hollow cylinder a lower velocity of the cylinder is obtained. So both cylinders have the same kinetic energy at the end, but the velocities are different due to the mass distribution. So equate the kinetic energies of two rolling cylinders with different mass distributions, and you will see that the linear velocity of the cylinder with a more mass away from the centroid will have a smaller linear velocity for the same amount of energy.

@@DrRans Thank you for your answer :) I see what you mean especially in a equation manner E= 1/2 (int(r^2)dm) .w^2 aka if you increase the r^2 you reduce w but velocity is w.r therefore velocity should be constant since mass is the same . Also forgetting about what we talked what is not intiutive about this concept ( I am not denying it or saying its wrong I am just trying to reaally understand it ). How exactly does at the t=0 moment the first rotation has more interia against the movement since ( again I know the formula and the basic linear logic from that but lets do it verbally) the partical at top sits very high and also since it sits high r is high , okey we say w is low but why exactly , what kind of nature forces cause this. Like it is the same mass there fore same total energy at t=0

@@rocketman99 At t = 0, both of the cylindars are at the same height, so they have the same potential energy (because their total mass is the same). Potential energy would be mass times height. Actually, there is a smal error here as the hollow sylindar has a higher centre of mass, so it actually has a little more potential energy than the solid cyinder, but even with this little extra energy, it has more resistance to rolling and thus rolls slower as a result of its resistance. To try an understand it verbally, it can be useful to think about the distance each bit of mass on the cylinder travels. In the hollow cylinder, in addition to the displacement in the direction of the ramp, mass is moving perpendicular as it is rolling. So the hollow cylinder, due to its larger radius, requires the mass to move perpendicular (lets call this up and down) relative to the ramp, and thus this added motion consumes some of the energy. So less energy is available for imparting velocity in the direction of the ramp.

@@DrRans thank you soo much that was really helpfull

Please look at p. 6 of Timoshenko and Goodier. They use the same approach (and elaborate on it a bit further) to derive this result and it is used throught that textbook and within the field of mechanics.

@@DrRans OK will do and thanks for the suggestion. You are correct that the principle of complementary shear stresses is widely used although I had no reason to question its generality until I saw your video. The T&G derivation is identical to yours so one cannot question it. Out of curiosity I will satisfy myself that some postulated stress distributions (say a 2 term polynomial) satisfies the various equilibrium equations etc. I guess the other way to demonstrate complementary shear stresses is via Mohr's circle. Thanks for posting the video.

@@DrRans 👍 thanks