Why is component reverse in Conical Pendulum?

[soccer5454]

Hello. In class today, we studied conical pendulum but I was confused at the part about its components. In all the diagrams ( http://dev.physicslab.org/img/90c0fb7a-ffb4-4573-b389-b50a559732c8.gif ) if shows The x-component as being sine, but I always thought x-comp was cos?? ( http://faculty.ccbcmd.edu/~jzelinsk/phys_101/chapter3/chapter3.htg/img2.gif )
Also for equations I made them

T cos(θ) = mv2/r
T sin(θ) = mg

But teacher say it is wrong and it should be other way but I don't understand, please help!

 

[TSny]

Often the direction of a vector is specified by the angle the vector makes with respect to the x axis, as in your second link. What about θ in your first link?

 

[soccer5454]

But even it was at a different spot, wouldn't the horizontal always be cos?

 

[TSny]

Look at the figure below. How would you use trig to find the lengths of the green and red sides of the triangle?

 

[soccer5454]

Green would be sin and red would be cos. so

T cos(θ) = mv2/r
T sin(θ) = mg

 

[TSny]

Green would be sin and red would be cos.

Yes, that's right.

so
T cos(θ) = mv2/r
T sin(θ) = mg

Which side of the triangle "points toward the center" of the circular motion of the pendulum bob?

 

[soccer5454]

Red line I believe

 

[TSny]

Where is the center of the circular motion in the picture in your first link? Is it to the left of the mass, to the right of the mass, above the mass, or below the mass?

 

[soccer5454]

I think its to the left

 

[TSny]

Yes.

So, according the the figure below, which component of the tension points toward the center of the circular motion? The green component or the red component?

 

[soccer5454]

Green comp

 

[TSny]

Yes. So, which component should be set equal to mv²/r?

 

[soccer5454]

sine!:)

 

[TSny]

Good.

 

[soccer5454]

Just a quick question,so the x-comp can always change? So it is not always cos or sin but it depends on where the center of motion is right?

 

[TSny]

The x component is not always obtained by using cos(θ). It depends on whether or not θ is measured from the x axis. Whenever you are in doubt, construct a right triangle and use trig to get the x and y components.

 

[soccer5454]

The x component is not always obtained by using cos(θ). It depends on whether or not θ is measured from the x axis. Whenever you are in doubt, construct a right triangle and use trig to get the x and y components.

Oh ok got it thanks :)