Answer
(a) $\omega = 0.430~rev/s$
(b) The turntable has spun through 0.068 revolutions.
(c) $v = 1.01~m/s$
(d) $a = 3.45~m/s^2$
Work Step by Step
(a) $\omega = \omega_0+\alpha ~t$
$\omega = (0.250~rev/s)+(0.900~rev/s^2)(0.200~s)$
$\omega = 0.430~rev/s$
(b) $\theta = \omega_0 ~t+\frac{1}{2}\alpha ~t^2$
$\theta = (0.250~rev/s)(0.200~s)+\frac{1}{2}(0.900~rev/s^2)(0.200~s)^2$
$\theta = 0.068~rev$
The turntable has spun through 0.068 revolutions.
(c) $v = \omega~(\pi~d)$
$v = (0.430~rev/s)(\pi)(0.750~m)$
$v = 1.01~m/s$
(d) $a_{tan} = \alpha ~(\pi~d)$
$a_{tan} = (0.900~rev/s^2)(\pi)(0.750~m)$
$a_{tan}= 2.12~m/s^2$
$a_{rad} = \frac{v^2}{r} = \frac{(1.01~m/s)^2}{0.375~m}$
$a_{rad} = 2.72~m/s^2$
$a = \sqrt{a_{tan}^2+a_{rad}^2}$
$a = \sqrt{(2.12~m/s^2)^2+(2.72~m/s^2)^2}$
$a = 3.45~m/s^2$
