Answer
The radial acceleration is $0.0257~m/s^2$
Work Step by Step
We can find the angular speed of the Earth as it rotates:
$\omega = \frac{2\pi~rad}{(24)(3600~s)}$
$\omega = 7.27\times 10^{-5}~rad/s$
We can find the radius of rotation for an object at a latitude of $40.2^{\circ}~N$ of the equator:
$r = (6.38\times 10^6~m)~cos~40.2^{\circ}$
$r = 4.87\times 10^6~m$
We can find the radial acceleration:
$a_r = \omega^2~r$
$a_r = (7.27\times 10^{-5}~rad/s)^2~(4.87\times 10^6~m)$
$a_r = 0.0257~m/s^2$
The radial acceleration is $0.0257~m/s^2$
