Question

An object of mass 10kg moves in a circular path of radius 0.5m with a speed of 3m/s.What is it's angular velocity

Answer 1

frequency = circumference/time = 2π*0.5/3 = π/3 seconds/rev

3/π rev/s * 2π rad/rev = 6 rad/s
or, more briefly,
ω = 2πf = 2π * t/(2πr) = t/r = 3/0.5 = 6 rad/s