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Let's assume we are rotating a boy in a circular path. If somehow the mass of the body changes(let's say some part of the object falls down). Will the angular momentum remain conserved in this case?

It is due to a doubt arisen i saw from a solution. There the condition was that the angular speed needed to be the same after some mass fell down. So,what was conserved there was centripetal force instead of angular momentum. Does that mean that falling of mass will have the same effect as external torque acting on the system?

What i learn from conservation of angular momentum is that if no torque acts on the system,then the angular momentum of the system is conserved. Here if some mass falls down,i don't understand why the centripetal force remains the same and the angular momentum does not. Kindly provide me with the proper concepts.

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  • $\begingroup$ when you say a body loses mass you have to specify exactly how it happens in order to get a unique answer. For example, a rocket is losing mass and depending on how fast the exhaust is moving it will gain different amounts of momentum. For a rocket the closest to 'deleting' the mass would be if it would just detach from the mass as it goes. In that case it would carry no momentum and the momentum of the rocket would be conserved. $\endgroup$ Nov 14, 2022 at 13:06

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If the angular speed, $\omega$, stays constant and some mass is lost which means that the moment of inertia about the centre, $I$, decreased then the angular momentum, $I\omega$, must also decrease.

The force causing the centripetal acceleration must also have decreased if the angular speed of what remains has been maintained at a constant value.

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  • $\begingroup$ Thank you very much for replying but why did $I$ decrease? Couldn't it be the case that $r$ has increased? If so,then how can we see that angular momentum changes? Let's assume $r$ has increased to neutralize the effect. $\endgroup$
    – madness
    Nov 14, 2022 at 8:42
  • $\begingroup$ Thank you but as i said we increase $r$,would that mean decrease of moment of inertia? $\endgroup$
    – madness
    Nov 14, 2022 at 8:49
  • $\begingroup$ Can't the condition $m_1r_2^2=m_2r_2^2$ be valid?If $m$ decreases then $r$ increases. $\endgroup$
    – madness
    Nov 14, 2022 at 8:49
  • $\begingroup$ It is due to a doubt arisen i saw from a solution. I think that one needs to see the question and the solution. As it stands your question is difficult to answer. $\endgroup$
    – Farcher
    Nov 14, 2022 at 9:02
  • $\begingroup$ The question,if i remember correctly,was this: An object of mass $m$ was being rotated in a circular path with a thread. At some instant,a portion of the object,say,$m'$ falls down. To keep the angular velocity constant,the length of the thread was increased. We needed to determine how much length was increased. And in the solution,centripetal force was conserved without any explanation. So,i am confused why that's the case. $\endgroup$
    – madness
    Nov 14, 2022 at 9:30

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