Motion of a Sphere: No Friction vs With Friction

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In the motion of a sphere on a horizontal surface, when no friction is present, the sphere moves purely translationally without rotation. However, when friction is introduced, it creates a torque that induces both rotation and translation. The applied force through the center of the sphere does not generate torque; instead, it is the friction at the contact point that causes rotation. There is a contention regarding the book's assertion that no rotational motion occurs under any conditions, leading to confusion about the role of friction. Ultimately, the discussion highlights the complexities of motion dynamics involving friction and the need for clarity in understanding torque generation.
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Homework Statement


A sphere is resting on a horizontal surface. A force parallel to the surface passing through the center of the sphere is applied.

Describe the motion of the sphere
1. Without any friction
2. With friction.



The Attempt at a Solution



When there's no friction, then the motion is purely translatory. But, if there is friction, it will apply a torque which will force rotation as well as translation. The second part isn't right though. Why?
 
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It cannot apply any torque, because the force goes right through the center of the sphere. What happens is that the friction touching the ball below is the culprit in creating this invisible torque.
 
The force initially applied does not have any torques but it is the friction itself that acts as a torque that rotates the ball equivalent to (frictional force*radius of the sphere)
 
Yeah, that's what I thought, but the book says that there can be no rotational motion under any conditions. I thought the book was wrong but maybe I'd missed something.
 

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