I have been struggling with Forces in a Cartesian Coordinate System and whether to understand what signs to put on to solve simple problems in the view of mathematics.
Let's make a simple one dimensional problem, in the y-axis.
I have an increasing $+yî$ direction up and we have gravity force that points down in the frame of reference. Most books will give it $\vec{F}_yî=m(-\vec{g})î$. Why is the minus sign only for the gravitational acceleration in the expression? Is it always opposite sign in the algebraic expressions in situations like this? Meaning $\vec{F}_yî$ has not a minus sign but the acceleration on the other side of the equation does. Even thou the force and acceleration is pointing down.
Does the unit vectors have any impact to tell in what direction the forces point and then declares it signs? Please help!