When forces are not aligned with axes, break them into components. If a force $F$ makes angle $\theta$ with the horizontal, then $F_x = F\cos\theta$ and $F_y = F\sin\theta$.

For a block on an incline of angle $\theta$, the weight splits into components parallel and perpendicular to the plane: $mg\sin\theta$ and $mg\cos\theta$. These components are key to motion and normal force calculations.

An object moving in a circle at constant speed still accelerates because its velocity direction changes. The centripetal acceleration magnitude is $a_c = v^2/r = \omega^2 r$, directed toward the center.

Centripetal force is not a new kind of force; it is the name for the net inward force required to produce circular motion. Gravity, tension, friction, or the normal force can supply it depending on the situation.