I do not understand at all why, if an object is sitting on a spinning platform, the friction force is towards the center. I understand the need for a centripetal force during circular motion, but friction is only in opposition to a force being applied to an object / system, why does it act as centripetal? I understand for a car, for example, the wheels providing the forces needed, but, for example, a penny sitting on a rotating disc, why would the friction be towards the center, would it not be in opposition to the impending motion of the tangential velocity? I have seen a lot of explanations on why there would obviously be a centripetal force, the need for one because there is a change in velocity, etc, but none of these explain why friction acts as this force, or how.
2 Answers
Static friction provides whatever force is necessary to stop the object from moving relative to the surface it sits on (up to a limit given by $\mu_s N$ where $\mu_s$ is the coefficient of static friction and $N$ is the normal force). In this case the coin (or whatever) sits on a surface which is accelerating inward - as described by the centripetal acceleration formula. To stop the coin from moving relative to that surface, static friction provides an inward force.
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$\begingroup$ Why is it accelerating inward? I know it is, due to the centripetal acceleration formula, but for all other systems there is a force pulling it inwards, (satellite - gravity, swinging ball - tension), etc. Stopping the coin from moving relative to the spinning disk, in that frame, would mean it would stop it from moving in the direction of its velocity, tangential to the circle. Where is the inward motion? $\endgroup$ Commented May 19, 2023 at 14:25
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1$\begingroup$ @VioletStrozykowski The piece of the circular disk that the coin sits on is indeed accelerating inward because of some kind of tension in the disk itself. The disk is a rigid object, meaning that there are internal forces that keep it held together, and this is what makes it possible for it to rotate without breaking apart. I was first only arguing that the piece of the disk that the coin sits on is accelerating inward. Then the coin receives whatever forces are necessary to keep it on that surface (basically the definition of static friction!), so the surface also gives it an inward force. $\endgroup$– AXensenCommented May 19, 2023 at 14:31
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1$\begingroup$ Oh, okay. So there is a kind of strain that is why the disk keeps accelerating, and the friction is analogous to sticking it to that in a way, so it also accelerates inward indirectly caused by the strain. That makes sense, I think. Thank you! $\endgroup$ Commented May 19, 2023 at 14:41
for example, a penny sitting on a rotating disc, why would the friction be towards the center, would it not be in opposition to the impending motion of the tangential velocity?
It would be in opposition of the relative motion between the surface it is sitting on, and the impending motion of tangential velocity.
That relative motion is equal and opposite to the centripetal acceleration of the penny around the center of the disk, and so that's the direction of the friction force.
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$\begingroup$ Opposite to the impending motion of tangential velocity would merely be in the opposite tangential direction, correct? This is still perpendicular to the inward force, though. The relative motion between the surface it is sitting on and the impending motion of tangential velocity wouldn't be inward, right? $\endgroup$ Commented May 19, 2023 at 14:31
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1$\begingroup$ @VioletStrozykowski the coin is moving tangentially relative to you, not relative to the disk. Static friction prevents motion relative to the disk, not motion relative to you (a somewhat arbitrary reference frame in this case). If you paint a red dot next to the coin, the coin does not move relative to that dot. $\endgroup$– AXensenCommented May 19, 2023 at 14:33