Recent content by PhysicsBoi1908

You could also get the constraint equations by putting the work done by string to zero, and then differentiating twice. This works here because the string is massless.

Ah! Thank you very much.

This is very clever. Thank you very much. I have a doubt though, in post #25 you concluded that the magnitude of friction per unit area will be constant, how did you arrive at that? More generally, how do we conclude that magnitude of friction is constant in any scenario?

Force will be applied on A. AC is the larger side, since ##\theta## is acute.

I think the author doesn't want us to think about internal forces at all when we consider an element of the lamina. Then for a radial element, the torque due to friction would remain constant. I'll think about this and post if something comes up.

That doesn't work either, I tried it just now. Also, the torque due to friction in case of A would be greater than in the case of B and C. Thank you for your help.

I did calculations assuming friction was concentrated at the COM. Here are the pics: The answer is incorrect. This approach also allows to write ##F_C## in terms of ##F_A## and ##F_B## individually (since ##\theta## is actually given), which shouldn't be possible.

I was given this question by my teacher when I didn't know the effective spring constant. My solution ended up deriving the effective spring constant by the end. I think I assumed elongation in springs 1 and 2 to be ##x_1## and ##x_2## respectively, and then drew the free body diagrams for the...

I have never seen this before. Thank you for showing this. What if I consider a radial element in the lamina, then the magnitude of acceleration of each point will be same for mass elements in it. Since the radial element is a system of mass elements comprising it, I need not consider the...

I think I got it. The non-uniformity is due to the internal constraint forces. But how can we be completely certain that there would be no non-uniformity, as you claim, in ##\mu dA \vec{f}##?

Hmm... the name did give me that vibe. But can we calculate it? Also, will it be uniform?

Internal constraint forces? I have never heard of this before... Can you please elaborate? I mean, I have used constraints to form equations, like for when a box falls down a wedge.

I am making too many typing mistakes right now. There have been more edits than comments. I guess I will go to sleep.

I have substituted ##\vec{f}## with ##\vec{\alpha}\times\vec{r_A}## where ##\vec{r_A}## can be written as a sum of ##\vec{r}_{COM}+\vec{r}##. ##\vec{\alpha}## is angular acceleration provided by torque ##\vec{l) \times \vec{F_A}##. I agree with your second statement. I have also corrected post #7.

With reference to post #3 and #4: $$\iint_S \vec{r} \times \vec{f} \mu dA = \iint_S \mu \vec{r} \times \vec{\alpha} \times \vec{r_A} dA = \iint_S \mu \vec{r} \times \vec{\alpha} \times \left( \vec{r_{COM}}+\vec{r} \right) dA =\not = 0$$ ##\vec{r}## is position of element from COM...