jbriggs444
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I do not think that this is a fruitful path to follow.gleem said:Perhaps, reanalyzing the situation where the sphere slips so the frictional force is divided into two parts one doing work as it slips resulting in the applied force providing the only torque, and one that does no work while working with the applied force to rotate the sphere. then take the limit as the friction goes to zero. Maybe?
If we decide that the surface is frictionless then there is nothing to divide into parts.
If we decide that the surface has friction then we need to figure out whether the coefficient of friction is sufficient for rolling without friction (in which case we already have a good approach) or insufficient (in which case we have a known and constant force that we can calculate with).
That part does not concern me at all. It is an engineering detail, unimportant to the mathematics of the situation. The idea of a yo-yo or a reel of 9 track mag tape is a good mental image.gleem said:I admit that the scenario of a bar being able to exert a torque without imparting some motion perpendicular to the direction of the force may not be physically realizable.
Sure. A spherical child's toy top being pulled from a string wound around its circumference and viewed from above.gleem said:I'm thinking that the situation with no friction may be as shown below in which case θ=X/R sort of a Yo-Yo situation. Think of the sphere sitting on a frictionless surface with its axis of rotation perpendicular to the surface.
View attachment 348532
But now there is nothing on the diagram to indicate how far the center of mass translates.
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