Vector components on Tilted Axis

AI Thread Summary
To find the components N_{x} and N_{y} of vector N in a tilted coordinate system, the correct formulas are N_{x} = -Nsinθ and N_{y} = Ncosθ. The negative sign for N_{x} indicates that the x component points in the negative x direction. This is due to the positive angle being measured from the y-axis towards the negative x-axis. If the angle were measured towards the positive x-axis, it would be negative, and the sign would adjust accordingly. Understanding the orientation of the angle is crucial for determining the correct vector components.
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Homework Statement



Find the components N_{x} and N_{y} of vector N in the tilted cooridinate system.


Homework Equations



cosθ = adg/hyp and sinθ= opp/hyp



The Attempt at a Solution



vectorconfusionc.jpg


The correct answer is supposed to be
N_{x} = -Nsinθ and N_{y} = Ncosθ

The error is on the component vector N_{x}.

How do you find the component vectors and come up with a negative for N_{x}?
 
Last edited:
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The x component of N is pointing in the -x direction.
That's what the minus sign is telling you.

You have to do this because the positive angle is measured from the y-axis and towards the negative x axis.
If you measured it towards the positive x-axis then the angle shown would be negative, and the sign would take care of itself.
 
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