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From Newton’s second law, $F=ma$, a massless object will always have zero net force. So can a massless pulley accelerate?

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2 Answers 2

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From a classical perspective, the acceleration of a massless object doesn't depend on the forces acting on it, it only depends on the kinematic constraints with surrounding masses. In short,

  1. Massless objects can have acceleration (including infinite)
  2. Forces acting on massless objects are always in balance

Of course, it sometimes leads to all sorts of paradoxes, which only tells us that massless object in classical physics is an abstraction.

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  • $\begingroup$ Got it, Thanks a lot. $\endgroup$
    – Eugene
    Apr 28, 2021 at 11:32
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Mostly objects with infinitesimal small mass arrange themselves in such a manner that the forces on them get balanced.

For example, let's talk about the reflection of waves with one end fixed and other end free (i.e. a massless ring attached to a rod). As the wave reaches the free end, the massless ring goes more than the amplitude of the wave. It does so to make the forces balanced.

Notice how the massless ring's displacement is higher than that of the wave's amplitude. It happens so that the string goes perpendicular to the rod and makes the forces balanced as there are no vertical forces left to balance out.

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  • $\begingroup$ What would happen if two forces with different magnitude is exert on a massless object in opposite direction? How would the forces be balance? $\endgroup$
    – Eugene
    Apr 28, 2021 at 11:34
  • $\begingroup$ @Eugene It depends on the kinematic constraints, either one force's magnitude increases or the magnitude of the other force decreases. For example in this case the Tension in the string is same but the normal reaction between the rod and the ring changes to adjust itself with the tension. $\endgroup$ Apr 28, 2021 at 11:41
  • $\begingroup$ Ok, got it thanks! $\endgroup$
    – Eugene
    Apr 28, 2021 at 11:54

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