Moment placed off-centre on a rotating body

Imagine a body which is allowed to rotated around its centre of gravity. I place a rotating moment, $$M_d$$ on a point which is a distance d from the body's centre. $$M_d$$ is only required to put the body in motion, i.e. overcome the friction and intertia required for the body to start rotating around its centre of gravity. Compare this moment to a moment $$M_0$$ located at the centre of gravity. Same conditions apply for $$M_0$$, it only has initiate rotation. Is $$M_0 = M_d$$? Or is one bigger than the other?

Theoreticaly they should be the same but intuitively when compared to screwing a screw, it is easier to screw the screw if you apply the moment directly on the screw axis of rotation. Could someone please explain if there is a theoretical difference or if it is only my intuition which is wrong.

• So why do you need a big flat screwdriver for big screws? By your analysis a small flat screwdriver is sufficient... – Solar Mike Feb 8 at 16:46
• I think the problem you are describing is more related to points of contact and grip? A larger screwdriver will have contact on the entire screw head compared to a smaller one, thus being able to transfer a larger moment. I wonder if not your answer together with kamran's answer is the one I am looking for. – loStraniero Feb 9 at 13:56
• No, the screwdriver will have two points of contact... – Solar Mike Feb 9 at 13:59
• Isn't half the surface of one side in contact together with half the surface of the other side? – loStraniero Feb 10 at 11:09
• Put engineer’s blue on a screwdriver and test. – Solar Mike Feb 10 at 11:19