Answer
Please see the work below.
Work Step by Step
We know that
$(\alpha)=18rp\frac{m}{s^2}=(2)(\pi)(\frac{18}{60})\frac{rad}{s^2}=1.885\frac{rad}{s^2}$
The angle is
$\theta=2(2\pi)=4\pi=12.566rad$
We can find the angular speed as
$\omega_f^2=2\alpha \theta$
This simplifies to:
$\omega _f=\sqrt{2\alpha \theta}$
We plug in the known values to obtain:
$\omega_f=\sqrt{2(1.885)(12.566)}=6.9\frac{rad}{s}$
(b) We can find the required time as
$t=\frac{\omega_f-\omega_i}{\alpha}$
We plug in the known values to obtain:
$t=\frac{6.9-0.0}{1.885}=3.7s$
