Recent content by Livio Arshavin Leiva

Very clear. Thank you.

I know but I couldn't reach that expression...

I think ##\Delta p## is considered as the variance of the momentum of the particle population. It should then be calculated as $$(\Delta p)^2=\left( \frac{1}{N}\sum_{i=1}^{N}p_i^2\right)-\bar{p}^2$$ but ##\bar{p}=0## since it's an ideal gas.

What's the procedure to get to that lagrangian?

If ##\omega=v_0/r##, then the ball should rotate at a fixed distance ##r## with the string not wrapping nor unwrapping around the post, right?

I was confused on what the statement of the problem meant by "tangentially". At first I thought it meant perpendicular to a line from the center of the post to the ball, but I guess it really meant simply perpendicular to the string. Because in case (b) the velocity of the ball is constrained...

I thought it was case (a), sorry.

Can I see the calculation?

Sorry, I thougth it was case (a). My bad. How can you prove that in case (b) the kinetic energy is conserved?

Then, angular momentum is not conserved? How can the radius change if the speed is never in radial direction? If the energy is conserved, what happens with the work done by T?

It would have to be ##C(T)\propto-T^-1##, right? In case the entropy is positive, this would mean the heat capacity needs to be negative.

If the radial distance of the ball to the post is reduced, and it does since eventually it hits the post, that means a translation exists in radial direction. In case (a), the tension of the string T is also in the radial direction, so this force is performing some work on the ball, because...

Yes, I checked those formulas and wrote the x and y components of the acceleration in the rotating frame, reaching the following system of entangled equations for x and y: \ddot x = 2\omega\dot y + x\omega^2 \ddot y = -2\omega\dot x + y\omega^2 Honestly I don't remember exactly how to solve this...

Actually I plotted the result I reached for R=1 and omega=1 and it looks like an spiral as you say: If I shift to a coordinate system anchored to the center of rotation I think the only difference is adding +R (in this case +1) in the "y" direction, isn't it?? I think formulating the...

Very nice... indeed it seems to be an equivalent scenario. I'll read a little and then compare results.