a) First example could be a $textbf{canon ball}$ which is not rotating because the sum of all torque on it is equal to zero, but is deaccelerating due to the force of drag.

b) Second equation could be a $textbf{motor axle}$, which is not translating anywhere because the sum of all forces acting on it is equal to zero, but is spinning faster and faster due to the torque acting on it.

Since we know that the only outside force acting on the book is its weight, we know that the book will reach $textbf{force and torque equilibrium}$ if the opposite force is put exactly at the spot where force of gravity is acting, which is its center of mass. This can easily be found by trying to balance a book on a single spot, when we reach the center of the mass, the book will be in equilibrium and the $textbf{pivot}$ on which the book rests will be marking the point where center of mass lays.

Penny left standing on the turntable will, due to the friction, start moving rotationally together with the record. As it is moving, centrifugal force will force it to the outern parts of the record. Or, better way to put it would be to say that lack of $textbf{centripetal force}$, which is directed inwards, will fail to change penny’s direction of velocity towards the inner parts and it will therefore, due to the $textbf{inertia}$, keep moving more towards a $textbf{straight line}$, which relative to the record seems as if its moving to the outern parts.