"Heavy" is a relative term when you hang something from the ceiling. A potted plant is heavier than a pendant lamp, a shelf filled with potted plants is heavier than a single plant, and an exercise swing with someone on it is heavier than all of these put together. You can use a different, easier method to hang a potted plant than you can to install an exercise swing.
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If your idea of heavy is just a few pounds, you might be able to get by with adhesive hooks, but realistically, it's safer to use toggle bolts for weights up to about 30 to 50 pounds. For loads greater than that, you need hooks screwed into a ceiling joist, but there's a limit on the weight a ceiling joist can support. For really heavy weights, such as your exercising body, you may need to go into the attic and install bracing.
Hanging Stuff From Toggle Bolts
A toggle bolt is the strongest type of drywall anchor. It consists of the bolt itself and a spring-loaded, folding metal bracket. When installed correctly, the bracket anchors itself on the back of the drywall when you tighten the bolt. That allows it to support a lot of weight, but the main limitation is the strength of the drywall itself. If you exceed the recommended weight of 50 pounds, the drywall can break.
You can install a toggle bolt anywhere on the ceiling. Just drill a hole in the drywall large enough to admit the folded bracket. Screw the bracket onto the end of the bolt and insert it through the hole. The bracket automatically unfolds behind the drywall. When tightening the bolt, maintain a little downward pressure to keep the bracket seated on the drywall and prevent it from turning.
Installing Ceiling Hooks
A ceiling hook is basically a lag screw with an open or closed hook on the end. You screw it into a ceiling joist, so the first step in installation is to locate a suitable joist using a stud finder. Joists are stronger near the wall plates than they are in the middle of their span, so if you have something really heavy, it's best to hang it as close to the wall as possible.
You need to drill a pilot hole for a ceiling hook to make the hook easier to install and prevent the joist from cracking. Use a drill bit with a diameter slightly smaller than the bolt shank and make the depth of the hole about three-quarters of the length of the shaft. When screwing in the bolt, you can usually get it started by hand, but you'll need the leverage of a screwdriver (the longer the better) to tighten it all the way.
Hanging Exercise Equipment
Two hanging options for exercise equipment are X-mount ceiling hooks and swing hangers that are held to a joist by two lag screws (not just one). For most equipment, you need two of these hangers, and they should be mounted to two different joists to distribute the weight.
Before you set up a swing in your living room, you should have your ceiling inspected by a contractor to make sure it can support the weight. If you overload a joist, it will sag and throw your ceiling out of alignment, assuming it doesn't break. Many factors affect the holding strength, including the joist material and dimensions and the location of the hook. If your joists can't support the weight, discuss bracing options with the contractor.