Hello sir

I'm having problems in the second part

If I analyse this in Ground frame, its clear that a1 is the centripetal acceleration. But while working in the CM frame, I considered the tangential acceleration, which means a1>centripetal acceleration. It had some extra acceleration as well. Can't understand why this is happening

Pls help!

@rohit1729 Hi

Hello !

Reading now ...

The centre of mass frame is a non-inertial frame, so working in that frame is going to be complicated as there will be fictitious forces present.

I must admit it's not immediately obvious to me how to write the calculation in the COM frame.

That's a hard question. Is it from the JEE Advanced?

not from any Previous year paper but I feel it's relevant

@JohnRennie , I've another qs sir

Hi :-)

A conical pendulum made of a rod (m,l) fixed at a point. It's rotating with constant angular velocity and maintains its angle with the vertical. Find the angle made by vertical.

In this question, if we write the torque equations from the hinge point , there's no torque to counter gravity---this is the problem im facing

Hmm, someone asked about this problem recently ...

You are quite correct, there is nothing to balance the torque due to gravity, but that's because there is an angular acceleration towards the centre.

The angular acceleration towards the centre is the centripetal acceleration.

So at equilibrium the torque due to gravity is equal to the centripetal torque.

It's the same way you analyse circular motion.

But isn't the centripetal acceleration provided by the hinge itself? And I'm observing it wrt the hinge? So torque due to that vanishes?

No, consider some element of the rod d𝓁 with a mass dm = ρ d𝓁

So that element is being acted on by a centripetal force dF = dm rω²

So there is a torque about the hinge dτ = x cosθ dF

Integrate from x = 0 to x = 𝓁 and you get the total torque due to the centripetal force.

(I can draw a diagram if this isn't clear)

Ah no! I'm familiar with this approach. But I still can't see why the torque isn't zero in a certain frame

Is this the [question] (physics.stackexchange.com/questions/546022/…) you were referring to?

The first answer seems to be addressing my doubt. That should mean there's an addition external torque which is there to keep such motion?

I need to go out now. I'll be back in a couple of hours.

Bye :-)

Ok :-)