# Insect-ring system, conservation of angular momentum

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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)

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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Doc Al
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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.

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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

Doc Al
Mentor
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.)

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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?

Doc Al
Mentor
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.

Gold Member
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!