Understanding Vector Components: Explaining an Inclined Plane Physics Question

[micaele]

So I was watching some of those physics videos posted in schoolwork board, and although he probably didn't make an error here, I don't think I understand it.

Here's the pictues. I'll elaborate after it so you guys know what I'm talking about:

http://img144.imageshack.us/img144/6632/88907417sb7.png When he broke the downward mg force into its components (mg cos theta = ma sub x and mg sin theta = ma sub y), shouldn't it be mg sin theta instead, and likewise for the other? I thought that when you break a vector into its parts, sine is associated with the y-axis and cosine for the x.

Maybe I'm having a brain fart, but I swear I had those vector components figured out.

Thanks ahead of time.

 

[Cyrus]

No. Draw a picture and work out the geometery. Your understanding of sin and cos is fundamentally wrong.

see "Right triangle definitions"
http://en.wikipedia.org/wiki/Trigonometric_function

Hopefully, you can work that out for yourself given the link.

 

[jtbell]

I thought that when you break a vector into its parts, sine is associated with the y-axis and cosine for the x.

It depends on whether the angle is measured from the x-axis or from the y-axis. If the angle is measured from the x-axis, what you wrote is correct. If the angle is measured from the y-axis, it's the other way around.

 

[micaele]

It depends on whether the angle is measured from the x-axis or from the y-axis. If the angle is measured from the x-axis, what you wrote is correct. If the angle is measured from the y-axis, it's the other way around.

THAT'S the reason!

Thank you, that completely did not occur to me. I understand now, thanks.

 

[TVP45]

One of the easiest (not fastest) ways to avoid this difficulty is to always use standard angle measurement (where the + x-axis is 0). Then x is always associated with cos and y is always associated with sin and the +s and -s take care of themselves.