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I was wondering if it is possible to have a pure planar rotation of a rectangular-prism shaped rigid body on a planar surface when it is subjected to a planar point force at the tip. Is there any range for the point force such that it can not break the static friction force (so no acceleration) but breaks the static friction torque around the center of mass (COM) of the body and thus, causes a pure rotational motion? I appreciate your answers with at least semi-theoretical proofs.

Thanks