PHYS121 Winter 2000
A student wrote:

I have a question I hope you can clear up.
If a block rests on a level plane, then the normal force (N) = - weight (W), which is mass (M) times acceleration due to gravity (g) where I am taking the y-component of g-vector to be a negative number.
If the plane is rotated to theta degrees, and the coordinate system lies parallel and perpendicular to the plane, how does this effect the N force? W=mg sin theta, so is N=-mg even though W is not on the y axis, or N=-mg sin theta even though W and N are not on the same line?

Prof. Seidler responds:

I disagree with your equation: W=mg*sin(theta). The weight force of the block is unchanged in magnitude and direction, W is still a vector that points straight down and still has length mg. In your selected coordinate system with y normal to the plane, the component of W along y is mg*cos(theta) {{ draw a picture to look at the trigonometry to see that it is cos(theta) not sin(theta) }}. As the normal force is the only other force along y and as the block has zero y-acceleration, you then have that the length of N = -mg*cos(theta).