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I came across a mechanics problem which is as follows:

enter image description here

I do not request for a solution to the problem but I have some doubts regarding it. I think that as no external torque is being applied at the centre of the circle the mass is rotating about so its angular momentum would remain constant. Thus, when its radius is halved, its velocity should become double by angular momentum conservation. This also gives me the right solution to this problem.

But what I don't understand is what force is acting on the mass which is changing its velocity. Tension is perpendicular to its velocity and the table is frictionless so how exactly is the mass's velocity changing?

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  • $\begingroup$ Note that images are not accessible to all users. Please edit the post by explicitly typing out the question rather than posting an image of it. $\endgroup$
    – BioPhysicist
    Commented May 31, 2021 at 12:34

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Tension is perpendicular to its velocity

This is the incorrect statement. If the mass is moving inwards its motion is not circular, so the tension force will have a non-zero component along the velocity, hence the change in speed.

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When the radius is decreased, the particle will somewhat spiral inwards. This causes a part of the tension to be along the velocity. This causes the tangential acceleration of the particle, increasing its speed.

There is a video by VSause, that explains this well. Here is the link: https://www.youtube.com/watch?v=_WHRWLnVm_M

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