Answer
(a) $v = 30~km/s$
(b) $\omega = 2.0\times 10^{-7}~rad/s$
(c) $a_c = 6.0\times 10^{-3}~m/s^2$
Work Step by Step
(a) We can find the speed of the earth.
$v = \frac{d}{t}$
$v = \frac{2\pi~r}{t}$
$v = \frac{(2\pi)(1.5\times 10^{11}~m)}{(365)(24)(3600)~s}$
$v = 30000~m/s = 30~km/s$
(b) $\omega = \frac{v}{r}$
$\omega = \frac{30000~m/s}{1.5\times 10^{11}~m}$
$\omega = 2.0\times 10^{-7}~rad/s$
(c) $a_c = \frac{v^2}{r}$
$a_c = \frac{(3.0\times 10^4~m/s)^2}{1.5\times 10^{11}~m}$
$a_c = 6.0\times 10^{-3}~m/s^2$
