Question

ω=120rev/min then it changed to 180rev/min in∆θ=4rev

first find angular acceleration and then find ∆t

Answer 1

$$∆θ=\omega_it+0.5\alpha t^2\\2∆θ=(\omega_i+\omega_f)t \\2(4)=(120+180)t\\t=1.6\ s\\ 4(2\pi)=(1.6)(120)\frac{2\pi}{60}+0.5(1.6)^2\alpha\\ \alpha=3.9\frac{rad}{s^2}$$