Rotation due to center of gravity

[JustAnotherNewton]

"The weight of an exercise book in picture A (where the centre of gravity is not on the axis of rotation) rotates so it moves towards the second position in picture B (where the axis of rotation goes through the centre of gravity). Explain why."

I don't believe any equations are necessary for this question.

I understand the pure concept of this question. The centre of mass/gravity is where all the weight of the object is centred, therefore it makes sense that an object would rotate to make that point central. However, I am struggling with the actual movement and position. For example, the book's centre of gravity is in the centre, so why does it rotate downward and then stop? The actual centre doesn't change position, so why does the book need to rotate?

I apologise if I haven't made it clear what I'm enquiring about, please let me know if further details are needed.

 

[Doc Al]

I apologise if I haven't made it clear what I'm enquiring about, please let me know if further details are needed.

Is the book constrained to rotate about some axis that does not go through its center of mass? If so, gravity will exert a torque about that axis.

A diagram might help.

 

[haruspex]

The weight of an exercise book in picture A (where the centre of gravity is not on the axis of rotation) rotates so it moves towards the second position in picture B (where the axis of rotation goes through the centre of gravity).

That makes no sense to me. If the mass centre is at some distance x from the axis of rotation, it will remain at distance x from the axis as the rotation occurs.
I suggest the statement should be referring to whether the line of action of the gravitational force passes through the axis, i.e. whether the mass centre's displacement from the axis is vertical.
As Doc Al posted, we really need to see the diagram or have a clear description of it.

 

[JustAnotherNewton]

That makes no sense to me. If the mass centre is at some distance x from the axis of rotation, it will remain at distance x from the axis as the rotation occurs.
I suggest the statement should be referring to whether the line of action of the gravitational force passes through the axis, i.e. whether the mass centre's displacement from the axis is vertical.
As Doc Al posted, we really need to see the diagram or have a clear description of it.

Sorry for the lackluster description. I have attached the diagram, if it helps.

 

[haruspex]

Sorry for the lackluster description. I have attached the diagram, if it helps.

It sure does.
You may be misreading the diagram. The axis of rotation is not the vertical dotted red line. It is horizontal, normal to the plane of the book, through the finger and thumb grip.
So the axis of rotation never passes through the mass centre.