Answer
a) $\omega=1.99\times10^{-7}rad/s$
b) $v_T=2.99\times10^4m/s$
c) $a_c=5.96\times10^{-3}m/s^2$
Work Step by Step
We have $\Delta t=3.16\times10^7s$ for $\Delta\theta=1rev=2\pi rad$ and $r=1.5\times10^{11}m$
a) The Earth's angular speed is $$\omega=\frac{\Delta \theta}{\Delta t}=1.99\times10^{-7}rad/s$$
b) The Earth's tangential speed is $$v_T=\omega r=2.99\times10^4m/s$$
c) The Earth's centripetal acceleration is $$a_c=\frac{v_T^2}{r}=5.96\times10^{-3}m/s^2$$
