How to calculate angular velocity and radius of a turn?
Your terminology is a little confusing, but I'm going to assume you're asking how to calculate turn radius and rate of turn based on airspeed and bank angle. These formulas can all be found in the FAA's Pilot's Handbook of Aeronautical Knowledge which is available for free online.
The Handbook gives the formulas for rate of turn and turning radius on page 4-34:
$$R=\frac{V^2}{11.26\tan\theta}$$
$$\omega=\frac{1,091\tan\theta}{V}$$
The variables used are:

$V$ = true airspeed in knots
$R$ = turning radius in feet
$\theta$ = bank angle in degrees
$\omega$ = rate of turn in degrees per second

For example, at 120 knots and a 30° bank angle, the turn radius and rate of turn are:
$$R=\frac{120^2}{11.26\tan30}=\frac{14,400}{11.26\times0.5773}=2,215 feet\approx\frac13nautical~mile$$
$$\omega=\frac{1,091\tan30}{120}=\frac{1,091\times0.5773}{120}=5.25°/sec$$
The &quot;magic constants&quot; in these formulas ($11.26$ and $1,091$) are conversion factors for the units involved (knots, feet, and degrees). Physicists would use unitless formulas involving $g$, acceleration due to gravity (roughly $9.8m/sec^2$).
You can also rearrange the formulas above using simple algebra to figure out the required bank angle given a desired rate of turn or turn radius.
Finally, note that things get a lot more complicated if you factor in winds aloft. Rate of turn will always be the same regardless of wind, but turning radius no longer applies because the aircraft will trace a spiral path along the ground, not a circle. The turn will be &quot;sharper&quot; on the upwind portion of the turn and &quot;wider&quot; on the downwind portion. This is why turns around a point is a complex maneuver taught in basic flight training: in order to fly a circular ground track, the pilot must constantly vary the aircraft's bank angle according to wind: lower bank angle upwind, higher bank angle downwind. The pilot must also use the rudder correctly to keep the turn coordinated at all times.
Other useful links:

Pilot's Handbook of Aeronautical Knowledge (quoted above)
Aviation Formulary has a section on turns
Standard rate turn article on Wikipedia
Banked turn article on Wikipedia

There are also some &quot;Related Questions&quot; over on the right-hand side of this page that might be useful.