Answer
$t=28.1s$
Work Step by Step
(a) We know that
$\alpha=\frac{\omega_f^2-\omega_i^2}{2(\theta-\theta_{\circ})}$
We plug in the known values to obtain:
$\alpha=\frac{(0)^2-(6.35)^2}{2(14.2\times 2\pi)}=-0.226\frac{rad}{s^2}$
(b) As $\alpha=\frac{\omega_f-\omega_i}{t}$
This can be rearranged as:
$t=\frac{\omega_f-\omega_i}{\alpha}$
We plug in the known values to obtain:
$t=\frac{0-6.35}{-0.226}=28.1s$
