Draw your half circle (or whole circle, doesn’t matter).
Make a guide of it (Cmd/Ctrl+5).
Draw a rectangle and copy-drag it as many times as you need.
Drag each rectangle down so that it snaps to the guide.
It helps to have Smart Guides turned on while you do all of this.
Here’s a picture of the job half done:
Elaborating on what Monika said, remember to use one less for number of copies, then Object>Expand, and Ungroup to work with each rectangle.
And as Steve said, Smart Guides are your friends (you can even snap to a normal circle with their help).
Follow Jacob's advice in the message above. Select your rectangles and from the Object menu choose Expand (or Expand Appearance which ever is available) and then use Ungroup to make a series of rectangles which can be moved seperately.
How to create quickly 15 rectangles touching each other without using CTRL+F and doing it by hand?
Copy-drag (drag with Option/Alt held down) the first time and then Cmd/Ctrl+D as many times as you need.