Hi!
I am going to assume all your objects are designs in all different sizes and shapes, right?
I will refer to them as 'designs' from now on.
And I will also assume you want to place them all around a circle.
1. Create a symbol (just read on, you'll see why)
Create a square the size of the biggest of your designs.
Then create a symbol from it. I know, you don't want to use a square, but wait, i am not done.
2. Create a circle
Next, create that circle.
Place an instance of the 'Rectangle' symbol you just created on top of the circles' topmost point.
Select circle and instance and align them horizontally.
3. Add guides
Place two guides, one horizontal through the circle's centre.
The other one is vertical, through the circle's centre as well.
So now you have a cross hair in the middle of the circle. The vertical one also goes through the centre of the instance of the symbol, right?
4. Rotating
Select the instance.
Next, type 'r' to activate the 'Rotate' tool.
Then click on the crosshair, where the two guides cross.
Rotate the instance as much as you need around the centre point of the circle. If you need a straight angle you can hold 'Shift'. The rectangle will be rotated 45 or 90 degrees.
To create a copy while you rotate, simply add the 'Alt' key. This means you hold both 'Shift' and 'Alt' while you rotate.
Release the mouse first, and the keys last.
You now have a copy that is rotated over the amount of degrees of your choice, and with the centre of the circle for reference.
Hit 'Ctrl-d' to repeat this step: you now have three instances. Continue until you have enough.
If you need really special angles you can use a radial grid.
5. Fun!
Then comes the fun part.
Create a symbol from each of your special designs, the ones you want to rotate around the circle.
Next, select the first 'rectangle' instance you want to change into one of your own shapes.
Go to the 'Symbols' panel.
Select the symbol you want to use instead of that rectangle.
Click on the 'Symbols' panel top right arrows to open the menu.
In the menu, choose 'Replace Symbol'.
The rectangle is now replaced with your special design AND the rotation is respected.
I hope this helps!