The angle of a rotating shaft turns in t seconds is given by theta= ω+1/2at^2

Question

and it is given that ω=3 2
rad/s and α=0.6 rad/s to complete θ=4 radians. Determine the time taken to complete θ=4 radians.

Answer 1

Theta = 4 Rad.
Wo = 3.2? Rad/s
a = 0.6rad/s^2

Theta = Wo*t + 0.5a*t^2 = 4 rads.
3.2t + 0.5*0.6t^2 = 4
0.3t^2 + 3.2t - 4 = 0
Use Quadratic Formula.
t = 1.13 s (Wo = 3.2 rad/s).
t = 0.125 s (Wo = 32 rad/s).

Answer 2

1.191s