Solving Tilted Axis Friction Problems

[Maximillien]

Okay I was just wondering exactly how I'm supposed to know of where to put my forces once I get them from what I'm given in the problem because I know how to break up for example the W in my problem into its components or units (I,J) I just don't know which direction to put them on the titled axis. Because for example on my picture the W Force is pointing down yet my book says = 16.38i - 11.47 j and the F force is pointing right but my book says the components are = -3.83i - 3.21j...

I got those numbers just not where they go on the tilted axes. Thanks in advance for any help.

 

[awvvu]

Remember that weight always points straight down, no matter how you rotate the axes. I guess you're doing that in the diagram, but it's hard to read it.

Are i and j still unit vectors in the unrotated axes or the rotated ones? I'm assuming the book means rotated, since weight is just in the j direction unrotated. So, you have to break up the weight force into components on your rotated axes. On the bottom picture, there should be the weight force along -i and -j. (assuming +i is up the ramp, +j is northwest perpendicular)