I am not able to understand how angular momentum is conserved. Without an external torque, the angular velocity will be constant. So, if I spin some object on some frictionless surface, it will keep spinning forever? But then, in section 18-2 Rotation of a rigid body, Feynman goes on to calculate the work done by the rotating object.
$$\Delta W=F_x\Delta x+F_y\Delta y$$(18.10)
When the object rotates, there is a change in the direction of velocity. So, without a constant external force, how can the body maintain its angular momentum? If without external torque an object will maintain its angular velocity, then how can we calculate "work done" by moving a certain degrees? Ie, if at 45 degrees it has a certain kinetic energy, it must be having the same energy after turning 50 degrees if we say angular momentum has not changed. How is it that here change in direction of velocity not considered as acceleration? What am I missing here?