Here v is the velocity of the sleeve along the rod as seen by the observer on the rod.
The Coriolis force is given by,
For understanding the origin of the Coriolis force see the solution for problem 1.112.
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.