Answer
(a) $a_{rad} = 15.1~m/s^2$
(b) $a_{rad} = 15.1~m/s^2$
Work Step by Step
(a) $\alpha=3~rad/s^2$
$r=\frac{40}{2}~cm=0.200~m$
$\theta=4\pi~rad$
$\omega^2-\omega_0^2 = 2\alpha ~\theta$
$\omega^2-0 = 2\alpha ~\theta$
$\omega = \sqrt{2\alpha ~\theta}$
$\omega = \sqrt{(2)(3.00~rad/s^2)(4~\pi~rad)}$
$\omega = 8.68~rad/s$
We can use $\omega$ to find $a_{rad}$
$a_{rad} = \omega^2~r$
$a_{rad} = (8.68~rad/s)^2(0.200~m)$
$a_{rad} = 15.1~m/s^2$
(b) $a = \alpha ~r = (3.00~rad/s^2)(0.200~m)$
$a = 0.6~m/s^2$
We can find the speed $v$ after two revolutions.
$v^2-v_0^2 = 2ad$
$v^2-0= 2a(4\pi~r)$
$v = \sqrt{2ad} = \sqrt{(2)(0.6~m/s^2)[(4\pi)(0.200~m)]}$
$v = 1.74~m/s$
We can use $v$ to find $a_{rad}$
$a_{rad} = \frac{v^2}{r} = \frac{(1.74~m/s)^2}{0.200~m}$
$a_{rad} = 15.1~m/s^2$
