So you are asking how much space you need in a circle with a rectangle in the middle for it to rotate? Here is an image drawn on a grid to help. My estimate is you need 30" all the way around it from the middle of the box plus a bit of clearance for your cabinet that is 15x24 to rotate. Note each square is 6".

Digging deep back into junior high school geometry (yep, I’m THAT old) the diagonal of the top of your cabinet is one side of the triangle with side A = 15” and B = 24”. A squared plus B squared equals the diagonal squared = 801. The square root of 801 is smidge over 28”. Cut a piece of cardboard or wood 29” long and rotate it in your intended space to be sure it clears (and my math is correct!)

That will be incrediby unstable. Look at all the Ikea lawsuits over dressers falling over because they were not secured to the wall. There is a reason that cabinet lazy susans are inside cabinets.

Wow everyone’s comment is very helpful! Thank you all. Including the ones regarding safety. I was planning on putting very light weight items in it and I suppose the lazy Susan base must be extra secured to the floor. I wonder if instead of connecting the two I should just leave it at the original size of one unit 15” wide and 12” deep if I spread them apart I could rotate them easily and perhaps mount some very light weight items on the back such as spices. Those could be mounted inside the cabinet door too. I suppose it might be best if I just posted the measurement of the size I’m working with and get suggestion and ideas on how to work with what we have?!

You might get good advice if you said what problem you're trying to solve. Is this in your kitchen? Are these cabinets you have that you're trying to re-use? Is it an odd space you want to fill?

This is just a bad idea. There are likely better ways to solve whatever problem you are attempting to solve. You are turning two shallow tall cabinets into a rotating double sided full depth cabinet. The rotation itself is going to require more room than the cabinet.

You could likely accomplish the same type of access with overextension drawer slides and pullouts. You could do hinged drawers that pull out and hinge open giving you drawers that essentially become two drawer sets 30" wide and 12" deep from a stationary 15" wide cabinet.

However, if you have to have a rotating cabinet for some reason... The only reasonable way to make it safe is to run a steel tube (conduit) from floor to ceiling and mount the cabinets to the tube using ball bearing pillow blocks. So long as the tube runs through the center of the lazy-susan and is properly mounted to floor and ceiling you will be safe.

I was planning on putting very light weight items in it and I suppose the lazy Susan base must be extra secured to the floor.

They are 6' tall cabinets... they are going to be massively unstable with feathers. Also there is no practical way to mount them to the lazy-susan to secure them. It is a 6' long lever, even empty the cabinets would likely tear themselves apart in a few rotations. It is just pieces of wood held together with screws and glue. To mount a 15" wide cabinet to spin it you are going to have to make it do things that wood, screws, and glue don't like doing.

First, your cabinets need to be wood or plywood, fiberboard isn't going to work and then you would likely need to epoxy in some all-thread and it is going to need to be deep (like 10"). Then you are going to have to secure it to a commercial grade lazy-susan or it is just going to rip that apart.

In the end, there is no way that is the most economical, useful or practical solution.

Phil Tritschler above mentioned that the square root of 801 is smidge over 28” - Being more accurate it seems the square root would be 28.30. If you're needing the calcuations to be perfect I'd say sticking to that is your best option.