Moving part of model on circle

Hi guys.
Need help with something.

I have imported model and I need to rotate part of it.
Here is what I mean.

I have this in the beginning:

And need to transform it to this (like when I press button I want this part of model to smoothly rotate until right angle):

So this is the code I used

//somewhere in the beginning
float angle = 0.0;

case GLUT_KEY_RIGHT:                                                                                                                          //when this button is pressed

int i, xo = 20;                                                                                                     // i is for loop and xo is x coordinate of the circle center 

	for (i=0; i<=object.vertices_qty; i++)                                                                     //go through all the vertices
		if(object.vertex[i].x > xo)                                                                         //if the x coordinate is bigger than xo - choose the part to rotate
		     if(object.vertex[i].r == 0)                                                             //calculate the circle radius if it hasn't been already done
		     object.vertex[i].r = object.vertex[i].x-xo;
		angle += 0.001;                                                                                      //increment the angle
                       //now I want to calculate new vertex coordinates (after rotation)
                       object.vertex[i].y = object.vertex[i].w + object.vertex[i].r*cos(angle);             //object.vertex[i].w is original y coordinate (before rotation) which is also coordinate of the circle center
		object.vertex[i].x = xo + object.vertex[i].r*sin(angle);

What is the problem here? The code is not working properly. The result is trash :D.

Sry if there are some serious mistakes. I am just a beginner in OpenGL and geometry is not my big friend :D.

Have a nice day

After some edits I ended with this but it is not working either.

			int i, xo = 20, yo = 2;
			angle += 0.1;
			for (i=0; i<=object.vertices_qty; i++)
				if(object.vertex[i].x >= xo)
					if(object.vertex[i].r == 0.0) 
					object.vertex[i].r = sqrt( (object.vertex[i].x-xo)*(object.vertex[i].x-xo) + (object.vertex[i].y-yo)*(object.vertex[i].y-yo)  );

				object.vertex[i].y = yo + object.vertex[i].r*sin(angle);
				object.vertex[i].x = xo + object.vertex[i].r*cos(angle);

Result is this:

You really need to look at matrices for these sorts of task. There is quite a lot of information on the web about this

Yea heard about them :D. Thanks for advice. I will look at that.

Hi it’s me again.
So I learned sth about matrices but still don’t know how to use them for this. I think it is not possible to change matrices during the polygons drawing. So how can I use them? Somehow apply them to the every vertex before drawing? How?

You don’t do it during the draw. You modify your vertices then draw

Ok so I use that loop and instead of that calculations use matrix multiplication to the vertex or vector.
Have to check more about that.
Thanks for help