Law of inertia in rotation Consider an object rotating about its own axis. If the law of inertia is applicable, the object should keep rotating with the same angular velocity if no external torque is provided, but how is the linear velocity of the particles of the object changing if there is not an external force, (Newton first law?)
Can someone explain where im wrong?
 A: 
but how is the linear velocity of the particles of the object changing if there is not an external force

You have to be consistent on what you term as a system.
If the system is the entire object, then there is no external force and the center of mass does not accelerate.
If the system is just one of the particles of the object, then there are forces external to the particle acting upon it, altering its velocity.
A: Instead of a rigid object, imagine two opposing masses on springs, spinning around the central axis.
The springs are what accelerates the masses, forcing them to go in a circle.
A rigid object is kind of like that, except instead of springs, it's held together by forces between molecules.
A: If you consider any individual particle in the rotating object, then it is subject to a centripetal force, and that is what makes the linear momentum of the particle change. The centripetal force is the resultant of the interactions between the particle and all the other particles that comprise the rotating object.
