Answer
(a) $\theta = \frac{2\pi}{5}~rad$ which is $1.26~rad$
(b) $d = (12~\pi)~cm$ which is $37.7~cm$
(c) $v = (3~\pi)~cm/s$ which is $9.42~cm/s$
Work Step by Step
(a) We can find the angle generated by P in time $t$:
$\theta = \omega ~t$
$\theta = (\frac{\pi}{10}~rad/s)(4~s)$
$\theta = \frac{2\pi}{5}~rad$
$\theta = 1.26~rad$
(b) We can find the distance $d$ traveled by P:
$d = \theta ~r$
$d = (\frac{2\pi}{5}~rad)(30~cm)$
$d = 12~\pi~cm$
$d = 37.7~cm$
(c) We can find the linear speed $v$ of P:
$v = \frac{d}{t}$
$v = \frac{12~\pi~cm}{4~s}$
$v = 3~\pi~cm/s$
$v = 9.42~cm/s$
