We had a lecture on the Coriolis effect today and I am very very confused, this is the first time I've heard of it as such. Anyway, I know that Coriolis acceleration is calculated by $\vec{a} = -2 \vec{\omega} \times \vec{v}$ where $\vert \vec{\omega} \times \vec{v}\vert = \omega v \sin\theta$. This gives $a = -2\omega v \sin \theta$. If I am given a latitude of say, 40°, how do I calculate the Coriolis acceleration of a moving object such as a bus in different directions like due south or due east?

Also, can I use $\omega = \frac{2\pi}{T}$ to calculate $\omega$? Would $T$ be the seconds in a day?