Now consider a noncentoidal rotation about O.

If a tangential force F passes through G, then,

where a_t is the tangential acceleration. The angular acceleration is given by,

Thus,

Since the force F is passing through the G, the moment of that force is about G zero. If it is so, from where do we get the moment ? From the reaction at the pin, of course.

Now, suppose a force F is applied at a point Q, which is at a distance of from O. Here k₀ is the radius of gyration about O i.e. the moment of inertia about O is given by .