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A ball is rolling in horizontal circles inside an inverted rough cone. In which direction does friction act?

I believe that for a rolling object on a rough surface, there is no friction in the direction of motion. Hence I think friction acts in the direction tangent to the surface, and must act in the direction up the surface of the cone because friction prevents the ball from slipping further down. Is this correct?

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  • $\begingroup$ Trying to understand your description. Isn't the ball both rolling in horizontal circles and at the same time descending in the cone due to gravity? I mean, are these pure horizontal circles? $\endgroup$
    – Bob D
    Commented Feb 4, 2020 at 21:21
  • $\begingroup$ @BobD I suppose it probably does descend in reality but in the exercise I am working on, it moves with constant angular speed in a horizontal circle of fixed radius and does not slip. $\endgroup$
    – A. Goodier
    Commented Feb 4, 2020 at 21:28
  • $\begingroup$ What would happen if you replaced the rolling ball with a sliding ice cube? How would the situation be different? $\endgroup$
    – BowlOfRed
    Commented Feb 4, 2020 at 21:29
  • $\begingroup$ @mvpq When I said "descend" I was not necessarily referring to slipping. I think at any instant you can consider the ball as being on the surface if an incline. There is then a component of rolling without slipping into/out of the plane containing the ball and incline and a component of rolling down the plane without slipping. It strikes me that static friction prevents the ball from sliding down the incline. But I could be wrong. $\endgroup$
    – Bob D
    Commented Feb 4, 2020 at 21:34

1 Answer 1

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A ball is rolling in horizontal circles inside an inverted rough cone. In which direction does friction act?

I think static friction, if any, will act in opposition to the component of the force of gravity on the ball acting down the surface of the cone to prevent the ball from sliding down the cone in a direction perpendicular to its horizontal rolling motion.

Hope this helps.

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