Relations between quantities describing circular motion
Since the arc length is s = φR, the linear speed formula gives υ = φR/t = ωR: the linear speed equals the angular velocity times the radius. The time for one full revolution is the period T: T = t/n, where n is the number of revolutions in time t; its unit is the second. The number of revolutions per unit time is the frequency ν: ν = n/t; its unit is 1/s (also called the hertz, Hz), and T = 1/ν. In one period a point covers the circumference 2πR and the radius turns through 2π rad, so υ = 2πR/T = 2πνR and ω = 2π/T = 2πν. So the angular velocity is inversely proportional to the period and directly proportional to the frequency.
“Clock hands”: find T for the tip of a clock hand (minute hand T = 1 hour = 3600 s, second hand T = 60 s) and compute ν. Safety: do not open the clock.