# Circular Motion - Newton's Second Law: Bead on a Rotating Hoop

• AzimD
In summary, the bead is rotating around an axis that the hoop is rotating around, and there is an inward force towards the center of the hoop.f
I understand the error in the OP and I agree with your explanation. It is a common misconception in introductory physics to consider centripetal force as some special force in itself. But any force, either a single force or a resultant can be centripetal. It does not have to be a resultant.
Even thought now I am not sure if the centripetal force that acts on a planet orbiting the star would qualify as applied or resultant. And the same for any other macroscopic force.

And I just don't see how calling it "applied force" make any sense. Especially when the label is "applied" to inertial forces or components of inertial forces which are not applied by anything.
It seems to be more misleading then useful.
@haruspex

If you look up "applied force" there are other definitions which seem to mean something else than a force that is not a resultant. True, these seem to be used in high school physics.
Accoding to this https://www.physicsclassroom.com/class/newtlaws/Lesson-2/Types-of-Forces tension or spring force are not applied forces. Neither gravity or electromagnetic force.
And according to this https://www.sciencefacts.net/applied-force.html the tangential component of the weight of a body on an inclined plane is the applied force.
This is why I don't feel that terms undefine, vaguely defined or unconsistently defined are useful, especially when we try to correct confusions or misconceptions. And if you define it simply as force that is not a resultant, there are hardly any of them in macroscopic physics, if you apply the definition consistently.

any force, either a single force or a resultant can be centripetal. It does not have to be a resultant.
The centripetal force is that component of the net force which is normal to the velocity. True, there may be only one force, and it may happen to be normal to the velocity, but I do not see how that special case constitutes an objection to the generalised version.
I just don't see how calling it "applied force" make any sense.
We do need a term to refer to those forces that add up to produce the net force. Can you suggest a better one?

jbriggs444
PhDeezNutz and PeroK
The centripetal force is that component of the net force which is normal to the velocity. True, there may be only one force, and it may happen to be normal to the velocity, but I do not see how that special case constitutes an objection to the generalised version.

We do need a term to refer to those forces that add up to produce the net force. Can you suggest a better one?
Why not just "forces"? The interaction between two objects is what we describe quantitatively by a force. If there is no interaction, then we have a special case and we need a special name, like "virtual force" or "inertial force" or whatever. This show that it is not really the same thing as the "force" as described above (result of interaction) but we like to use it as if it were. But why do we need a special name to name the same thing which was already defined simply as "force"? And if we have the result of more than on interaction, we call it "net force", which is the result of the superposition of individual interactions, each one described by a "force" (which we have already defined).

But of course, if a name (or in general, a world), is used quite frequently, any discussion is useles. The use makes the rule. I suppose you did not make up the term yourself. Is there any reference of a textbook where they use "applied force" with this meaning?

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Chestermiller