Insect-ring system, conservation of angular momentum

AI Thread Summary
The discussion revolves around a circular ring with an insect moving along its periphery and the conservation of angular momentum. The key point is that while the insect moves, the net torque about the center of the disk remains zero due to internal forces, allowing angular momentum to be conserved for the entire system. Participants clarify that the reaction force from the disk on the insect creates an equal and opposite torque, reinforcing the concept of system-wide torque balance. The confusion about torque and system dynamics is resolved, leading to a clearer understanding of the principles involved. Overall, the conversation emphasizes the importance of recognizing internal forces in analyzing angular momentum conservation.
Krushnaraj Pandya
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Homework Statement


A circular ring (2m, R) with a small insect of mass m on its periphery, is placed upon smooth horizontal surface (axis of rotation passing through center and perpendicular to the ground i.e disk is lying horizontally)
. The insect starts moving with velocity v w.r.t ground along the periphery. The angular velocity of rotation of ring is (note*-I just have a problem with one step of the solution)

Homework Equations


net torque=dL/dt

The Attempt at a Solution


I got the correct answer as v/2r by conserving angular momentum about O (center of disk). What I don't understand is how the net torque about it is zero- surely, the insect must have had to give an impulse to rotate the disc at w from rest, even if for a short time
 
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Krushnaraj Pandya said:
What I don't understand is how the net torque about it is zero- surely, the insect must have had to give an impulse to rotate the disc at w from rest, even if for a short time
You are correct. Note that the angular momentum of the system is conserved, not the angular momentum of the disc alone.
 
Doc Al said:
You are correct. Note that the angular momentum of the system is conserved, not the angular momentum of the disc alone.
I get that all the forces are internal- but we can't say the disk will apply an equal and opposite 'torque' on the insect can we? then how can we say the net torque is zero
 
Krushnaraj Pandya said:
but we can't say the disk will apply an equal and opposite 'torque' on the insect can we?
Why not? Note that the torque is about the axis of the disk. (Just like a point mass can have angular momentum about some point, forces exerted on it may produce a torque on it.)
 
Doc Al said:
Why not? Note that the torque is about the axis of the disk. (Just like a point mass can have angular momentum about some point, forces exerted on it may produce a torque on it.)
from what I understand, you're trying to say the reaction force of the disk on the insect exerts the equal and opposite torque about the central axis, am I right?
 
Krushnaraj Pandya said:
from what I understand, you're trying to say the reaction force of the disk on the insect exerts the equal and opposite torque about the central axis, am I right?
Right. Thus the net torque on the system is zero and angular momentum is conserved.
 
Doc Al said:
Right. Thus the net torque on the system is zero and angular momentum is conserved.
Oh! I get it now, I had confusions about how systems and torques related here...but it's all clear now. Thanks a lot!
 
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