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But here's my issue, in particular if the set up looks like this http://www.cs.utah.edu/~zachary/isp/applets/SlidingBlock/image1.gif, the incline is FRICTIONLESS!, and my coordinate system is set up in such a way that the block will be moving in the POSITIVE direction on the x-axis (when it gets moving that is). Say the angle here is 30 degrees. When resolving the weight vector into the x and y components, how do you account for the fact that gravity/acceleration is a vector (has direction and magnitude)? I understand that w=ma. The way I reason is that if you're trying to find the y-component of vector w, this is w=m(-9.8)cos(30), which makes sense because the y-component vector is directed in the negative direction in relation to the y-axis. But (HERES MY PROBLEM) if you resolve the weight vector into its x-component the same way, w=m(-9.8)sin(30), you get a negative number obviously indicating that the block is moving in the opposite direction that it should be. And this doesnt make sense. Other books simply dont account for the sign on the acceleration vector but rather look at the vector as a whole: example

y-comp is w=-m(9.8)cos(30)

x-comp is w=m(9.8)sin(30)

which gives the correct direction of movement for the x-component. While this gives the correct magnitude and direction, my issue is why doesn't such an x-component equation account for the negative sign for acceleration/gravity, because acceleration/gravity is a vector. This is driving me nuts.

Thanks