Will a sphere on a frictionless surface rotate if pulled by a string at the top?

[mbrown3391]

http://cheeseparade.com/diagram.png

Imagine a sphere on a frictionless surface. A string is attached to the top of the sphere, as shown. If a force is applied to the string, how will the sphere move? Will there be any torque at all, even though there is no friction? Or will the sphere move in exactly the same way as if the string was attached to the side of the sphere?

 

[A.T.]

Will there be any torque at all, even though there is no friction?

Sure. Your scenario is equivalent to a sphere floating in space. If the force doesn't go through the center of mass, it will start rotating.

 

[mbrown3391]

Ok, that's what i figured. But will there be translational movement as well? If so, how can you describe the force that acts on the center of mass as a function of the force that acts at the top of the sphere?

 

[A.T.]

But will there be translational movement as well?

Yes

If so, how can you describe the force that acts on the center of mass as a function of the force that acts at the top of the sphere?

They are the same

 

[mbrown3391]

Ok, thanks for you help!