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For a particle in circular motion about a point due to a central force, is it correct to say that "net force on the particle is 0"?

Obviously there is a force on the particle defined by the equation of central force $f(r)\hat r$, and I would not like to consider centrifugal force as any real force so that the concept of net force can't even exist. There is only one force and that is central force. However, in the frame of reference of particle it is at rest, so the net force would be 0.

What is the net force acting on the particle in this case then?

BioPhysicist
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SHINU_MADE
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2 Answers2

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In an inertial frame of reference, circular motion requires a non-zero net force, since the particle is accelerating.

In a non-inertial reference that moves with the particle, the particle is at rest, so its acceleration is $0$. Your options are then:

  1. Throw out Newton's second law: $F\neq ma$ in this frame
  2. Throw out Newton's third law: introduce pseudo-forces that do not have an "equal but opposite reaction", but then we can allow $F=ma$ to be true as the pseudo-forces cancel out the real forces acting on the particle. This is typically how the analysis is done for accelerating reference frames.

So it depends on which frame of reference you want to do the analysis in and which of Newton's laws you want to keep if you choose to work in a non-inertial frame.

BioPhysicist
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2

When you say net force, one means the sum of all forces that act on the object at any instant of time over the course of it's motion. In the strictest sense, if you mean to talk about the time averaged value of the net force on an object for some specific time interval, you must explicitly state that you are referring to the average value, further, you need to specify the interval over which the force is averaged, e.g. the average value of the central force in your example is not the same over a quarter of a rotation as it is over the entire cycle.

Albertus Magnus
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