What happens to KE when lowering a raised book? I understand the conservation of energy theorem and mechanical energy, but there is this question that confused me a bit, so I hope someone explains it.
If you had a book and you raised it, you gave it energy (its potential energy increased as it rises). Then you lower the book, so the potential energy changes into kinetic, but then what happens to that kinetic energy?
 A: Suppose you raise your book to a height.
Here as you said the potential energy of book will increase.
now what happens if I let the book go down?
The potential energy will now convert into kinetic energy and hence the potential energy of the book will decrease.
 Now  what If I stop the book in the midway by catching it before it touches the ground?
When you catch the book ,because of the collision of the book and your hand the kinetic energy of the book  will convert into now sound and heat and the book will now stop.
In summary the kinetic energy of the will convert into heat and sound.
A: to raise a book, you need to apply some force on the book. the gain of energy is related to the force and on how high you raised the book. then if you drop the book, it will fall with some velocity hence gain some kinetic energy. at a given point in its fall, it will have lost as much potential energy as it has gain kinetic one. 
if you want, the potential energy is "transformed" into kinetic energy
A: Potential energy is the theoretical energy available, if you decide to make use of it, hence "potential". Physical energy is lost as you lower an object (eg. friction, if you are driving a car down a slop), and the object attains a new potential energy.
Of course, in a thought experiment, lowering an object requires no energy change at all, but a hypothetical thought object has no potential energy anyway!
