Recent content by PiEpsilon

Unfortunately I have just received rejection letter, as I do not fulfill the entry criteria. Is it really the grim reality that person with my circumstances have all the doors shut to academic institutions? At this point I can confidently say I ran out of ideas to improve my chances to be...

[Post edited by a Mentor] I really don't want to get into discussion as it is not the topic I am asking about. Maybe I shouldn't mention it in the first place but I believed it would make my situation more coherent. The fact is, I did everything I could to get the best out of the situation...

That would be the next logical step. However it seems unlikely until the whistleblower matter does not resolve (which could be 2-3 years, if ever). Unfortunately the medical treatment and recovery quickly drowned any funds that would allow me to continue studying there (it was one of the main...

I have not completed my undergraduate degree. I did some some courses in the home country but left without completing the semester. Things started to finally get better while I was taking courses in the US (actually it was great) but got knocked down by health emergency. Right now I am trying to...

Thank you for reply! I apologize for vagueness of the post, but the situation is really something I am not comfortable writing about. Putting things bluntly the academia and education system I was (un)lucky to attend is corrupted, racist and hostile towards anyone different. I never played...

Greetings everyone! After many attempts and fails I believe I have fallen between the cracks of the education system. I would appreciate any advice how I can get back on the right track and continue my formal education. I am residing in the Eastern European country. I have finished high...

Thank you for checking this! I appreciate your help.

Summing everything up: Initially the bar with the flywheels rotates about the x-axis. Initial angular velocity and angular momentum are collinear and point along that axis too. After the ball is dropped it produces an angular impulse that changes the angular momentum. Reasoning as in the first...

From the Euler's equations: ##\dot\omega_{z0} = -A\omega_x\omega_{y0} ## (I will keep denoting ##\omega_{y0}\equiv\omega_y (0)## although I should have left it unchanged for ease of reading) ##\omega_{y0} = L_y/I_y = 0.0059/0.13 Js^{-1}kg^{-1}m^{-2}\approx 0.0454s^{-1}##Therefore...

Let's see... Initially the figure rotates about the x-axis. During the collision torque acts in the x-y plane. Angular momentum about the z-axis is then zero at all times. However the figure clearly rotates about that axis as it aligns itself with angular momentum vector ##\vec L## At time ##t...

From the Euler equations: ##I_x\dot\omega_x = (I_y - I_z)\omega_y\omega_z## ##I_y\dot\omega_y = (I_z - I_x)\omega_z\omega_x## ##I_z\dot\omega_z = (I_x - I_y)\omega_x\omega_y## Since ##I_y = I_z##, we have: ##\omega_x = const.## ##\dot\omega_y = (1 - I_x/I_y)\omega_z\omega_x## ##\dot\omega_z =...

Oh right! The Euler's equations should do it. The answers for these quantities are: ##\Omega_n = 154s^{-1}## and ##r = 1.77 \times 10^{-2}cm## I am not sure why angular velocity has no angle measurement units.

What we know: The ball is dropped at the tip A with some speed ##v_0## and rebounds with speed ##v##. This collision produces an angular impulse, changing the angular momentum of the bar with the flywheels. Solution inspired by an answer provided by @TSny in the similar question. Angular...

Thank you for an elaborate answer. The result agrees completely if one assumes ##m << M##. I have suspected that the final speed of the particle must be different but the textbook answer put me off the track. I guess it is a lesson to check it only after fully understanding the problem.

I am still unsure I follow. Consider the rotating disk system. Then the only force producing torque is from the 'bouncing' particle. Since it is a contact force, it is normal to the disc surface at all times during the collision. I have ignored any torques arising from friction forces between...