Recent content by Norashii

I have already seen proofs of this problem, but none of them match the one I did, therefore I would be glad if someone could indicate where is the mistake here. Thanks in advance.**My proof:** Take a limit point x of U that is not in U, but is in K (in other words x \in K \cap(\overline{U}-U))...

It means that it is a cone trunk without thickness

Yes, but the CM shifts only vertically if you keep the mass dm constant and just change it's height. However if you deform and the deformed part becomes denser then the CM should move to the denser region, it is like a compression am I wrong?

Yes, the mapping seems right and about the density, thinking a bit more I believe that it has to change even for a small ##b##, because if it stayed constant the ##CM## wouldn't be displaced in the ##x-y## plane which is something that should happen.

I'm really sorry for the imprecision, actually you can consider ##b << h## such that the density does not change significantly and can be considered approximately constant.

Linearly, but there is no explicit expression given.

Yes, for a regular complete cone you can use the symmetry and ##x_{cm}=y_{cm}=0##, for the ##z## coordinate you can just use cylindrical coordinates ##z_{cm}=\frac{1}{M}\int_{0}^{2\pi}d\theta\int_{0}^{h}\int_{0}^{z\frac{R}{h}}z \rho(z) \mu d\rho dz =...

I couldn't make progress in this problem, I would appreciate some suggestion on how could I attack this problem. Thanks in advance!

Hi, I'm a undergrad second year physics student, I love physics since elementary school and dream of becoming a researcher in Mathematical Physics. I hope I can add to this community but I don't consider my self too smart, sorry for it.