Question

If the thrower takes 0.90 s to complete one revolution, starting from rest, what will be the speed of the discus at release?

Answer 1

ω₀ = the initial angular velocity (from rest)
t = 0.9 s, time for a revolution
θ = 2π rad, the angular distance traveled

Let
α =  the angular acceleration
ω =  the final angular velocity

The angular rotation obeys the equation
(1/2)*(α rad/s²)*(0.9 s)² = (2π rad)
α = 15.514 rad/s²

The final angular velocity is
ω = (15.514 rad/s²)*(0.9 s) = 13.963 rad/s

If the thrower's arm is r meters long, the tangential velocity of release will be 
v = 13.963r m/s

Answer: 13.963 rad/s