Recent content by Dale

Excellent, except that you will want those as vectors, not just the magnitudes. So for the rotating $$v_l(t)=(-\omega l \sin(\omega t),\omega l \cos(\omega t))$$and for the translating $$v_l(t)=(0,v)$$ Then, the next two steps are as follows. First, write the velocity ##v_l(t)## for a ruler...

I think that you need to work through the math for yourself. Why don’t you do it for the example you posted. Let’s simplify that the ruler is a rigid line of length ##L## and mass ##m##. Use the variable ##-L/2 \le l \le L/2## to identify points on the ruler, with ##l=0## being the CoM. Now...

I agree. I think we have explained it every way possible. @gen x just needs to actually sit down and do the math.

No, you specified So there is no change to the motion. We are only changing how we decompose the motion into translation and rotation. The motion is a vector field, specifically the field of the velocity of each tiny piece of the object. You can decompose a vector into x and y components...

So what? Just because they are internal doesn't mean that they don't exist. The usual way is to redefine your system so that the internal force of interest becomes external. We can place the boundaries of our system anywhere we like, and we can analyze multiple systems. This is the completely...

Inside the ruler there is tension. As it is spinning the material of the ruler is under stress. The motion tries to pull the ruler apart, and the tension inside the material holds it together. If you spin the ruler fast enough, or if the ruler is fragile, it is possible for the material to...

Yes, this is all correct. This is not correct. The CoM moves along a straight line in any case, regardless of our choice of center of rotation. If we choose another point as the center of rotation (call it B) then B will not move along a straight line, but B is not the CoM. There is a...

The center of rotation certainly can translate. Did you not see the plots that I posted? They show what it means. You can pick any point and decompose the motion as a translation and a rotation about that point. That is what those graphs show.

Because the distance between the primary and the satellite can change. And if they are not both tidally locked then the distance between points on either object also changes.

Please be aware that personal speculation is not permitted here. There is no part of either classical electrodynamics or quantum electrodynamics that corresponds to this statement. At least not to my knowledge. Nor is there any need for such a claim. Poynting's theorem covers energy...

I think that more important than a label of rotation vs revolution you should focus on rigid vs non-rigid motion. Rigid motion can be decomposed into a rotation about any arbitrary point and a translation. Non-rigid motion can not generally be decomposed into such simple motions at all. The...

You can ask “which center of rotation makes my analysis easiest”.

The point is to show that any point can be chosen as the center, if desired. You have freedom to choose the center. You misunderstand. All of those plots show the same motion of the same object at the same time. In all three plots the axle is in the center of the wheel and the wheel is spinning...

To support this see the plots I posted below

On PF, AI output is not considered to be a valid source, and this thread is an excellent example why. What you posted is an AI hallucination, and because you didn't know the material you didn't recognize it as a hallucination. In my personal opinion, it is AI's reputation that is more in...