anuttarasammyak's latest activity

It seems not necessary. For any angle configuration we get the same result.

The contraposition: "E[ X ] converges thus E[ |X| ] converges" seems easier to handle. $$ E[|x|]:=\int_{-\infty}^{+\infty} f(x)|x| dx =...

Integral for even n diverges clearly to plus infinite. Integral for odd n is zero for integrand [-L,L]. However we do not have such a...

For my interest what Pet stands for and what role does it play ？

Sure. The Second Newton is ##m\boldsymbol {\dot v}= \boldsymbol R.## Here ##\boldsymbol R =R\boldsymbol e_x## stands for the tension...

it seems yes

A disk of radius ##r## is wrapped with an inextensible massless string. A particle of mass ##m## is attached to the end of the string...

I am sorry for my poor English. Tension force is zero. The wire outside the disk is straight and becomes short with pace ##r\Omega##...

I try to make the Lagrangian. Say coordinate of m is (X,Y) $$X=r \sec \phi \ \cos (\theta - \phi) $$ $$Y=r \sec \phi \ \ sin (\theta -...

Thanks.　 For x/r ##\rightarrow \infty##, the purple force decreases so ##\dot{x}## would also decrease. For x=0 wire tension cannot...

I see. Tension from the wire (blue) generates centripetal force (green) for circulation of m. The rest component (purple) causes...

Does the wire wrapping direction wrt ##\Omega## matter in your result ? It seems that one tighten and the other loosen the wire.

https://www.feynmanlectures.caltech.edu/II_29.html is a good one to know the fundamentals.

Applied magnetic field should be perpendicular to the velocity of the particle so that its track is a circle not a spiral.

Some alpha particles could be on circle track in constant kinetic energy and come back to the heavy source with a designed homogeneous...