If water stays in a pail of water that is whirled around a circular path, the water stays in the pail. But is it because of centripetal force or inertia? I'm getting confused by all the different answers i get from different sources.
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$\begingroup$ see this related question: physics.stackexchange.com/questions/108925/centrifugal-force $\endgroup$– pentaneCommented May 3, 2016 at 12:30
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1$\begingroup$ They're just two different ways of describing the same phenomenon. "Centrifugal force" is part of a mathematical description of what it would feel like if you could sit in the bucket. "Centripetal acceleration" is part of a mathematical explanation of what you would see if you stood off to the side and watched somebody else swing the bucket over their head. $\endgroup$– Solomon SlowCommented May 3, 2016 at 18:47
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3 Answers
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If a body of mass m hanged on a string is moving, let uniformly, on a circle fixed relatively to the ground, then an observer G on the ground uses the 2nd Newton Law : $$ \mathbf{F}=m\cdot \mathbf{a} \tag{01} $$ and finds the relation between the force $\mathbf{F}$ and the acceleration $\mathbf{a}$. For observer G there exists a "real" force, the tension of the string. This force is the centripetal force which is pulling the body continuously to the centre. Of course $\mathbf{a}$ is the centripetal acceleration. Observer G is justified to use the Law since he(or she) is on an inertial system of reference (called also Newtonian system).
For a massless observer B on the body there exists also the "real" force $\mathbf{F}^{\prime}=\mathbf{F}$, the tension of the string. The body is motionless relatively to him so $\mathbf{a}^{\prime}=\mathbf{0}$. Observer B meets a contradiction using 2nd Newton Law : $$ \mathbf{F}^{\prime}=m\cdot \mathbf{a}^{\prime}=\mathbf{0}, \quad \textbf{FALSE} \tag{02} $$ This is due to the fact that the system of observer B is accelerated relatively to the inertial system G, so it's not an inertial system and B is not justified to use the 2nd Newton Law. In order to use the Law it's necessary to introduce a "virtual" force $\mathbf{A}^{\prime}=-m\cdot \mathbf{a}$ and apply the Law: $$ \mathbf{F}^{\prime}+\mathbf{A}^{\prime}=\mathbf{F}-m\cdot \mathbf{a}=\mathbf{0}, \quad \textbf{TRUE} \tag{03} $$ This force $\mathbf{A}^{\prime}$ is a so-called inertial force and in our case is the centrifugal force which observers on the body feel to push them away from the center. Generally inertial forces appear in non-inertial systems and they are introduced in order to apply correctly the Newton Laws in these systems.
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$\begingroup$ so this means the inertial force A' which is the centrifugal force is what keeps the water in the pail ? @Frobenius $\endgroup$– Al-Commented May 3, 2016 at 17:16
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$\begingroup$ @Al- : What happens depends who observer you are : (a) If you are the observer G on the ground, you don't see any centifugal force. You have a centripetal force $\:\mathbf{F}\:$ (in our case that exerted by the walls of the pail on the water) which forces the water to move on a circle. (b) If you are the observer B on the pail you see the centrifugal force $\:\mathbf{A}^{\prime}\:$ to cancel the centripetal force, so you see the water and the pail in rest relatively to you. $\endgroup$– VoulkosCommented May 3, 2016 at 18:07
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$\begingroup$ does this mean centripetal force is what keeps the water in the pail or inertia? $\endgroup$– Al-Commented May 3, 2016 at 18:27
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$\begingroup$ @Al- : Please read my answer and above comment. ".....; and asking the right question is frequently more than halfway to the solution of the problem." W.HEISENBERG in PHYSICS AND PHILOSOPHY, 1958. $\endgroup$– VoulkosCommented May 3, 2016 at 18:36
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$\begingroup$ I did read your answer multiple times but as i said all the different answers are confusing and yours isn't clarifying either as you are not giving me a clear answer. $\endgroup$– Al-Commented May 3, 2016 at 18:45
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Note that you have to swing the pail with a certain minimum speed for the water to stay in. That minimum speed is such that when the pail is at the top of the arc, the rope accelerates the pail downward faster than gravity accelerates the water downward. Otherwise, the water falls out.
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If water particles move in a circular path its because of some net force towards the centre. This net force is usually called "centripetal force".
Don't ever put centrifugal force into the description. It is not a force, but just a name of the "feeling" that your body (or in this case water particles) want to move out of the circular motion but can't.
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$\begingroup$ but let's assume inertia is the centrifugal force even if centrifugal force doesn't exist but it would be the opposite of centripetal force right? $\endgroup$– Al-Commented May 3, 2016 at 17:10
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$\begingroup$ @Steeven : However, see the "obligatory xkcd" in the 1st comment in the link posted by pentane. $\endgroup$ Commented May 4, 2016 at 6:26