The tangential velocity of an object is directly proportional to the radius of the circular motion. How come orbital velocity is inversely proportional to the radius?
Orbital velocity generally is the pre-requisite velocity necessary for a satellite to stay in orbit. It is the minimum velocity necessary to keep the satellite from falling into the planet.
The shorter the radius of orbit, the closer the satellite is to the planet which it orbits, and the greater the gravitational attraction which must be overcome for it to remain in orbit. So a shorter radius means greater velocity required.
A longer radius puts the object farther out in space in weaker gravity and requires less velocity to keep it from falling into the planet. So a longer radius means less velocity required.
Tangential velocity is a result, not a pre-requisite. It is a function of the size of the circle the object describes and the number of rotations per unit time it makes. The larger the circle, the greater the distance which must be covered during each rotation. So if the object makes one rotation per minute, a longer radius means more distance covered during that minute, and greater velocity.
Greater orbital velocity results in more rotations per unit time. The orbital velocity is a requirement or pre-requisite for staying in orbit, whereas tangential velocity is a result of circular motion.
In other words, when you compute orbital velocity you specify the number of revolutions per unit time necessary to stay in orbit. This requirement becomes omega (rotations per unit time) in the tangential velocity formula.