If there is no slipping between the cylinder and the planks then,
From (4) and (3) we have,
Newton single handedly brought about a new era in our understanding of the physical world, through his famous equation F = ma and the law of gravity. These laws successfully predict the behavior of all phenomena from the microscopic world to the astronomical world! Ofcourse, Einstien changed things once again but that was only after about 4 centuries. Solving Irodov dramatically helped me understand the power, elegance, simplicity and beauty of Physics. Hopefully you will enjoy the journey too.