Say you have a mass on a string being twirled around in a circle by your fingers at a constant angular velocity , and then you increase its angular velocity . What are the forces involved that increase the angular velocity of the mass? I first thought that one needed a torque to increase the angular velocity but can one really apply a torque on a piece of string?
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There are two options: either your fingers move, or the string bends (or both).
When you use your fingers to make something spin, you actually have to move your fingers in a circle to make it accelerate; you can't do it while leaving the fingers in place. The tension of the string no longer points towards a center: it has a tangential component, which provides the torque.
If instead the string is attached to the shaft of a motor and you increase the speed, the part of the string closer to the center will start to move faster, which will make it bend and have a bit of a curve. This will again provide a tangential force, and the mass will accelerate until it catches up and the string is straight again.
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$\begingroup$ Many thanks Javier . So are you saying that the tension in the string is pointing ahead of the instantaneous circular position of the mass ? So what we have originally is a mass moving around in a circle with an instantaneous centripetal force via the tension in the string. Then the fingers suddenly push the string forward its previous position , causing a tangential tension force component (because the string is suddenly in its new position) that accelerates the mass linearly. Doesn't this mean there isn't a torque? $\endgroup$– DubiousAug 29, 2020 at 17:51
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$\begingroup$ @Dubious your description is right, but there is a torque, because there is a force component perpendicular to the position vector (measured from the original center, not from wherever the finger is). $\endgroup$– JavierAug 29, 2020 at 18:38
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$\begingroup$ Javier - isn't a real physical torque on a pivoted solid object virtually the same as the string problem above? A force may be applied close to the pivot causing some deformation (just like the string) and there is some tensile tangential component of the force being channelled all the way through the medium of the object to its peripheral end? $\endgroup$– DubiousAug 30, 2020 at 16:09
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$\begingroup$ @Dubious They're not exactly the same. An ideal string only makes a force when it's fully stretched, and the force is in the direction of the string. But a rigid object can have shear stresses; that is, a force not perpendicular to the surface of contact (imagine a ball attached to the end of a pole). It doesn't have to deform to transmit the force, unlike a string. $\endgroup$– JavierAug 30, 2020 at 22:31