Explanation:
Given:
[tex]\omega_0[/tex] = 10 rev/s = [tex]20\pi\:\text{rad/s}[/tex]
[tex]\omega[/tex] = 15 rev/s = [tex]30\pi\:\text{rad/s}[/tex]
[tex]\theta[/tex] = 60 rev = [tex]120\pi\:\text{rads}[/tex]
a) the angular acceleration [tex]\alpha[/tex] is given by
[tex]\alpha = \dfrac{\omega^2 - \omega_0^2}{2\theta}[/tex]
[tex]\:\:\:\:\:\:\:=\dfrac{(30\pi)^2 - (20\pi)^2}{240\pi} = 6.5\:\text{rad/s}^2[/tex]
b) [tex]t = \dfrac{\omega - \omega_0}{\alpha} = \dfrac{30\pi - 20\pi}{6.5} = 4.8\:\text{s}[/tex]
c) [tex]t = \dfrac{\omega - \omega_0}{\alpha}[/tex]
[tex]=\dfrac{20\pi - 0}{6.5} = 9.7\:\text{s}[/tex]
d)[tex]\theta = \frac{1}{2}\alpha t^2[/tex]
[tex]\:\:\:\:\:\:\:=\frac{1}{2}(6.5\:\text{rad/s}^2)(9.7\:\text{s})^2 = 305.8\:\text{rad}[/tex]
[tex]\:\:\:\:\:\:\:= 48.7\:\text{revs}[/tex]
