If you have a ball spinning on a string which is attached to a pole, will it keep spinning in the absence of any friction/air resistance/other retarding forces?

I'm trying to think about this in terms of Newton's First Law which suggests that the ball will keep trying to rotate, causing tension in the string and maintaining circular motion. Intuitively however it seems impossible that giving the ball a starting push would enable it to keep spinning around in a circle forever.

But on the other hand objects in orbit will continue to stay in orbit since the force of gravity is continually pulling them inwards whilst they continue to try and move in a circular orbit.

I would really appreciate any explanations to help me, at this point just very confused.

  • $\begingroup$ Intuitively however it seems impossible, your intuition is based on the practical conditions, but in absence of any retarding force (ideal conditions) the ball will keep rotating forever $\endgroup$ – Letsintegreat Jan 18 at 9:26
  • $\begingroup$ Thank you for the response. Could you please go into why it will keep rotating forever? What sustains the tension force in the string? The reason I ask is because Newton's First Law specifically references objects moving in a straight line in the absence of a net force, whereas in this example the ball is moving in a circle with the net centripetal force acting on it. $\endgroup$ – latin333 Jan 18 at 9:31
  • $\begingroup$ The vertical component of tension force is balanced by the weight of the ball, while the horizonal component of tension is always in the direction perpendicular to the velocity of the ball (Horizonal component points towards the center of the circular path, while velocity is always tangent to the path), which means net force in the direction of velocity is zero, hence speed of the ball will remain conserved forever, as there are no retarding forces. $\endgroup$ – Letsintegreat Jan 18 at 9:35
  • $\begingroup$ Thank you that makes a lot of sense. What would happen if you hit the ball tangentially? $\endgroup$ – latin333 Jan 18 at 9:36
  • $\begingroup$ If we hit the ball tangentially, then its velocity will change, hence required centripetal force will change, and string would have to re-configure itself, so as to balance weight by one component, and provide centripetal force with the other, the ball will eventually start rotating in a fixed circular orbit $\endgroup$ – Letsintegreat Jan 18 at 9:39

In the complete absence of any friction/dissipative forces (i.e. no friction in the pivot, no air resistance, no flexing of the string) then conservation of energy says that once the ball has been started it will continue in motion for ever. The string constrains the ball's motion, but the force exerted on the ball by the string does no work since it is always perpendicular to the string's velocity, so the ball's energy does not change.

The reason this answer is not intuitive is that achieving a complete absence of friction is very difficult in practice. For a start, you would have to enclose the ball, string and pivot in a vacuum to eliminate air resistance.


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