If the resulting trajectory of the charged particle is a circle, what is ω, the angular frequency of the circular motion?

For this answer you need to have in mind the following formulas:

Fmag = qvB

Also have in mind that Centripetal acceleration is: ar = v2/R

centripetal force will be : Fc = mv2/R

And velocity is: v = ωR

Remember that the magnetic force is the centripetal force then:

Fmag = Fc

qvB = mv2/R

qB = mv/R

Next you need to substitute for velocity:

qB = mωR/R

qB = mω

ω = qB/m