A scanner floats when the artificial gravity in a shuttlepod fails
Artificial gravity is a collection of systems designed to mimic the gravity of a planet so that working in space is easier. One of the first uses of artificial gravity on Earth ships was in the 1990s on ships such as the SS Botany Bay and cryonics satellites. (TOS: "Space Seed"; TNG: "The Neutral Zone")
The basis of the Federation's artificial gravity technology was a "flying belt" found in a Slaver stasis box. (TAS: "The Slaver Weapon")
Elaysians have difficulty adjusting to the gravity of other worlds because their home planet has such low gravity. Without surgery, they need to utilize a special chair or braces to allow them to move. (DS9: "Melora")
The USS Enterprise-D was equipped with a low-gravity gymnasium. (TNG: "Encounter at Farpoint")
Artificial gravity is created using generators embedded in gravity plating on the floor. Gravity levels in corridors and crew quarters could be adjusted. (DS9: "Melora"; VOY: "Learning Curve") Shuttlebays were "variable gravity areas." (Star Trek: The Next Generation)
Artificial gravity failures
When the Xyrillians were draining power from Enterprise NX-01 in 2151, the gravity in Captain Archer's quarters went offline while he was taking a shower. (ENT: "Unexpected")
In 2152, the Enolians attacked and boarded Enterprise's shuttlepod, arresting Captain Archer and Commander Tucker and leaving the shuttle adrift. When Enterprise found it, the artificial gravity was off line. (ENT: "Canamar")
After being attacked, the Kronos One's artificial gravity field failed, and the whole ship experienced weightlessness for several minutes while assassins boarded and killed several members of the crew, including Chancellor Gorkon. (Star Trek VI: The Undiscovered Country)
Cardassian station Empok Nor's artificial gravity was off line when Elim Garak first boarded the station, but he repaired it before the rest of the team came aboard. (DS9: "Empok Nor")
In 2372, during a battle with the Pralor the USS Voyager lost artificial gravity on deck 8. (VOY: "Prototype")
In 2374, a Species 8472 creature deactivated artificial gravity on deck 5 of Voyager while it was injured. (VOY: "Prey")
In 2376 when an electromagnetic lifeform was affecting ship's systems, the USS Voyager temporarily lost artificial gravity on Deck 9. The only injury reported was that "Ensign Mulcahey" bumped his head on the ceiling." (VOY: "The Haunting of Deck Twelve")
Parts of the artificial gravity system
Background
Artificial gravity was one of the technological concepts invented for the original series. This allowed for actors to stand up and walk around normally instead of being flown on wires or anything else that would be costly to do on a weekly television series. It was rationalised that even if everything else had failed on the ship, it would be one of the last systems to go.