What would be the effect of applying two parallel forces of the same value at opposite points of the equator inside a sphere?

Common sense tells me that it wouldn't move, but it seems that it could cause a torque from the point of contact with the ground that may not be balanced with the rolling resistance. I mean, would it create movement if

$$ 2Fr \gt \delta mg $$

where $F$ is the force applied at one of the two points, $r$ and $m$ are the radius and the mass of the sphere, $g$ is the gravity force and $\delta$ is the rolling resistance coefficient.

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Then imagine that the two forces are created by two internal motorized wheels (blue schema).

  • $\begingroup$ Are the forces directed towards the center of the sphere or tanget to the surface? $\endgroup$
    – pp.ch.te
    Apr 26, 2017 at 19:34
  • $\begingroup$ Tangent to the surface, sorry for not specifying $\endgroup$
    – SrJaimito
    Apr 26, 2017 at 20:10
  • 1
    $\begingroup$ What exerts these forces? Do you have a small levitating rocket engine in there, then sure, it could roll. Do the forces come from something mounted onto the sphere, then it won't. $\endgroup$
    – Steeven
    Apr 26, 2017 at 20:48
  • $\begingroup$ It would be good if you could add a sketch if the setup. As I read it, the two forces are pushing at two opposite points inside the sphere and then you mention rolling friction which is a very varying type of force. Would you mind sketching out your thinking? $\endgroup$
    – Steeven
    Apr 26, 2017 at 20:51
  • $\begingroup$ @Steeven ok, just give me a moment... $\endgroup$
    – SrJaimito
    Apr 26, 2017 at 20:54

1 Answer 1


Fore everey force there is an equal and opposite reaction. Put the reaction forces onto the blue object. In a perfect configuration the blue wheels cannot move relative to the sphere, so the summed forces acting on combined system (of blue wheels and black sphere) is zero. As it is zero the system (sphere plus wheels) will not be inclined to move due to these forces.
If the blue wheels do move inside the sphere, however, then it is a different matter. You would need to consider both the acceleration fo wheels relative to sphere and changes to the center of mass of the system that could cause it to roll.


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