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I know that the centripetal force of an object points towards the centre of rotation of the object.

But lets say I have a ball moving inside a cone in a fixed circular path. Where is the centripetal force pointing to? It is friction which should be the centripetal force but I feel like we could take the right force as well to be some part of the centripetal force. Now which of the two is correct and to where will this force point? The vertex of cone, the actual centre present on the plane of the circle formed by the rotation or above or below that plane.

Another scenario. Lets say I have a ball tied to string and rotate it, BUT not in a plane. The thread also traces a cone open towards the ground. Here the tension also points towards the vertex of the cone. But the gravity pulls it downwards. Is the centripital force ONLY the tension or a combination of both the tension and the gravity? If it is the latter do we have to just find the resultant vector of the tension in the rope and the gravitational force to get the centripital force.

Edit 2: Uploading my free body diagrams (probably incorrect though)

enter image description here

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  • $\begingroup$ Have you drawn a free body diagram for either scenario? $\endgroup$ Commented Jun 9, 2023 at 10:35
  • $\begingroup$ What do you mean by a "fixed circular path"? Isn't the ball spiraling down? $\endgroup$
    – Bob D
    Commented Jun 9, 2023 at 10:37
  • $\begingroup$ @ChetMiller yes but not sure if they are correct. $\endgroup$ Commented Jun 9, 2023 at 10:46
  • $\begingroup$ @BobD i don't really think it should necessarily be spiralling down. The friction may be enough to stop if from moving inwards. $\endgroup$ Commented Jun 9, 2023 at 10:48
  • $\begingroup$ let's see them, and let's see the corresponding force balance equations. $\endgroup$ Commented Jun 9, 2023 at 10:48

1 Answer 1

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In both cases the ball is moving in a horizontal circle, so the centripetal force must also be horizontal.

In the first case (cone) the centripetal force is the sum of the horizontal components of the normal force and friction. The vertical forces on the ball - which are the vertical components of the normal force and friction and also the weight of the ball - net to zero.

In the second case (string) the centripetal force is the horizontal component of the tension in the string. The vertical forces on the ball - which are the vertical component of the tension and the weight of the ball - once again net to zero.

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  • $\begingroup$ Oh I see, thanks. $\endgroup$ Commented Jun 9, 2023 at 10:58

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