How to draw a coordinate system

[Optikspik]

Homework Statement

If i want to show which direction is "positiv" I can do like this right? (Or is it wrong)

2. But if the figure would look like this, could i draw a coordinate system rather?

Is this way to show which way i say as positive? or should i rather draw like this?

Or Is it not possible to draw a coordinate system like this? If it is easier to have right as positive and down as positive in y-axis way?

PLease help me sort this out. Mostly second question

 

[DEvens]

As long as you do things consistently, you can have nearly any coordinates that are convenient. So any of the choices you have illustrated here would be acceptable, as long as you then use those coordinates correctly.

So in the first case, it seems like you mean for the mass M moving straight down to be positive, and the mass m to be moving up parallel to the ramp to be positive. As long as you then apply this correctly, it is completely ok. You have to keep in mind that it means that the tension of the rope is pulling in the positive direction for one mass and the negative for the other. And that it is pulling parallel to the coordinate, but that it is not at the same angle in full 3-D space.

In the next case, you are doing something similar for the two blocks. Again, as long as you apply this consistently, it is ok.

And in the final example, you have an x and a y. You can choose the positive and negative directions as you like, again as long as you apply it consistently.

 

[Optikspik]

Yes so positive y can be downwards and positive x can be rightwards?