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Below is a diagram of a simple pendulum with a 'fixed pivot point' and a rigid spherical mass $m$ attached to the end of a string.

I have shown the forces acting on the mass, its weight $mg$ and the string tension ($T1$ and $T2$) for the 2 snapshot positions.

I have also drawn a red line along the equator of the spherical mass to show its change in spatial alignment between the 2 positions.

My question is where are the forces that would cause the mass to change its alignment (spin) in space?

I'm assuming that 'mg' and 'tension' forces are acting through the COM, therefore they cannot be causing this 'spin'.

enter image description here

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The string itself also provides a tangential force at the point of contact, which is responsible for the rotation of the object.

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If the string were to swing freely without the mass attached then it would have a different natural period from the pendulum with the mass attached, because it has a shorter effective length.

Therefore in the pendulum configuration the mass must exert a force on the string to drive it to swing with a different period. By Newton’s third law the string exerts an equal and opposite tangential force on the mass, and it is this tangential force that causes the mass to rotate with each swing.

Another way to see this is to realise that the string cannot remain perfectly straight throughout each cycle of the pendulum, but will actually bend slightly at the extreme point of each swing. This bend in the string means that the string’s tension is not perfectly radial, but has a small tangential component which rotates the mass.

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  • $\begingroup$ I think your final paragraph might be off. This would happen even with a rigid pole instead of a string. $\endgroup$
    – BioPhysicist
    Commented Sep 18, 2020 at 3:29
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    $\begingroup$ @BioPhysicist A rigid rod could exert a tangential force on the mass through its fixed point of attachment without bending. The string cannot - its point of attachment acts like a pivot. Hence the string must bend. $\endgroup$
    – gandalf61
    Commented Sep 18, 2020 at 4:53
  • $\begingroup$ But a rigid pole can tolerate tangential stress, while an ideal string cant, so it would have to bend. This explanation seems fine to me. @BioPhysicist can you elaborate as to why its wrong? $\endgroup$
    – dnaik
    Commented Sep 18, 2020 at 4:53
  • $\begingroup$ Sorry, the last part made it seem like you were saying the bending caused the rotation $\endgroup$
    – BioPhysicist
    Commented Sep 18, 2020 at 11:10
  • $\begingroup$ So that last paragraph is just to prove how a tangential component can be created to make the mass swing back and forth (pendulum motion). But the actual 'spin' is caused by an equal and opposite eccentric force on the mass by the string at the point of attachment. $\endgroup$
    – Dubious
    Commented Sep 18, 2020 at 14:46

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