Visualizing the Motion of Coins on a Rotating Scale

[haruspex]

is it correct to write the normal force on the coin at the part of rod with the rod's value of g at that point since they are going to be sticking onto the rod?

I think you mean the rod's value of acceleration at that point.
Yes. If at some point less than 2L/3 from the axis the normal force is zero then the coin must be accelerating faster than the rod, which is not possible. So N>0, which means the coin must be in contact with the rod.

 

[Rahulrj]

I think you mean the rod's value of acceleration at that point.
Yes. If at some point less than 2L/3 from the axis the normal force is zero then the coin must be accelerating faster than the rod, which is not possible. So N>0, which means the coin must be in contact with the rod.

I am not sure if you got what I meant, for example I am interested in finding acceleration that coin experiences at say L/3
so the equation will be, N - mg = -ma and my doubt is whether if it is correct to write a = g/2? as it is the acceleration rod has at that point

 

[haruspex]

correct to write a = g/2?

Yes, that must be right. If it were more, it would penetrate the rod; if it were less it would lose contact with the rod, making N zero, so then it would fall at rate g and immediately catch up to the rod again.

 

[zwierz]

There is a funny counterintuitive fact: if $m$ is a total mass of all coins then $$|\epsilon|\sim const \,m^{1/3},$$ as $m\to\infty$ where $\epsilon$ is angular acceleration of the rod right after it is released. Other parameters are fixed.