Gravitational potential energy (U) is the energy stored in an object-Earth system because of position in a gravitational field, equal to U = mgh near Earth's surface or U = -GMm/r in general, where the reference point (U = 0) is set at infinity. It changes by ΔU = -W done by gravity.
Gravitational potential energy is energy stored in a system because of where an object sits in a gravitational field. Lift a book off the floor and you've done work against gravity. That work doesn't vanish, it gets banked as potential energy the system can cash in later as kinetic energy when the book falls.
In AP Physics C: Mechanics you need two versions. Near Earth's surface, where g is basically constant, U = mgh (you pick where h = 0, and only changes in U matter). For satellites, escape problems, or anything far from a planet's surface, you use the general form U = -GMm/r, where U = 0 is defined at infinity. The negative sign isn't a mistake. It says a bound object has less energy than a free one, so you'd have to add energy to pull the masses apart. The deeper connection that makes this Physics C and not Physics 1 is calculus: gravity is a conservative force, so F = -dU/dr. The force is the negative slope of the potential energy curve, and U is the negative of the work gravity does as the object moves.
Gravitational potential energy lives at the heart of Topic 3.3 (Conservation of Energy) and feeds directly off Topic 3.1 (Work-Energy Theorem). Because gravity is conservative, the work it does depends only on start and end positions, not the path. That's exactly what lets you write K₁ + U₁ = K₂ + U₂ and skip the kinematics entirely. On the exam, energy conservation with U is usually the fastest route to a speed, a height, or a maximum compression, and it's often the only practical route when acceleration isn't constant.
It also shows up in rotational contexts tied to Topic 5.4. A rod swinging down from a pivot or a ball rolling down a ramp converts gravitational potential energy into both translational and rotational kinetic energy, so U = mgh (measured at the center of mass) becomes the input side of a rotational energy equation. If you can track where the potential energy goes, you can solve most of Units 3 and 5.
Keep studying AP Physics C: Mechanics Unit 5
Conservation of Energy (Unit 3)
GPE is one of the main accounts in the energy bank. When only conservative forces act, ΔK = -ΔU, so whatever potential energy the system loses shows up as kinetic energy. Every 'find the speed at the bottom' problem is really a GPE bookkeeping problem.
Work-Energy Theorem (Unit 3)
Potential energy is defined through work. The work gravity does on an object equals -ΔU, and in calculus terms F = -dU/dr. If an FRQ hands you a U(r) graph or function, differentiate it (and flip the sign) to get the force.
Gravitational Field (Unit 7-adjacent gravitation problems)
Near Earth's surface the field g is uniform, so U = mgh works. Far from a planet the field falls off as 1/r², so you must integrate, and that integral gives U = -GMm/r with U = 0 at infinity. Picking the wrong formula for the situation is a classic point-loser.
Nonconservative Force and Thermal Energy (Unit 3)
Friction breaks the clean ΔK = -ΔU exchange. With friction in play, mechanical energy isn't conserved, and the missing GPE becomes thermal energy. Energy FRQs love asking you to account for exactly where that energy went.
No released FRQ needs the phrase 'gravitational potential energy' in the prompt for it to be the whole game. Energy-conservation FRQs are a Physics C staple, and GPE is almost always one side of the ledger. Expect to: set up K₁ + U₁ = K₂ + U₂ for objects on tracks, pendulums, or springs-plus-gravity systems; use U = -GMm/r to find escape speed or orbital energy in gravitation problems; recover force from a potential energy function with F = -dU/dx; and split a falling object's GPE into translational plus rotational kinetic energy when something rolls or swings. In multiple choice, watch for sign traps (work done by gravity vs. change in U) and for questions checking whether you know U = mgh only works when g is approximately constant. Always state your reference point for U = 0; readers look for it.
They're related by a sign flip, and that sign flip costs points constantly. The work gravity does equals the negative of the change in potential energy: W_grav = -ΔU. When an object falls, gravity does positive work and U decreases. If you put work done by gravity AND a ΔU term in the same energy equation, you've double-counted gravity. Use one or the other, never both.
Gravitational potential energy is stored energy due to position in a gravitational field, and only changes in U are physically meaningful.
Use U = mgh when g is approximately constant near a surface, and U = -GMm/r for satellites, escape velocity, or anything where distance from the planet changes significantly.
U = -GMm/r is negative because U = 0 is defined at infinity, so any bound object has negative potential energy and needs added energy to escape.
Gravity is a conservative force, which means W_grav = -ΔU and F = -dU/dr, so you can recover the force by differentiating the potential energy function.
In conservation of energy problems, lost GPE becomes kinetic energy (translational, rotational, or both) unless a nonconservative force like friction converts some of it to thermal energy.
Always state where you set U = 0 before writing an energy equation; it's a required setup step on FRQs.
It's the energy stored in a system because of an object's position in a gravitational field. Near Earth's surface it's U = mgh; in general it's U = -GMm/r with U = 0 at infinity, and it changes by the negative of the work gravity does.
Because the reference point U = 0 is set at infinite separation. A bound object sits below that reference, so its U is negative, meaning you'd have to add energy to pull the two masses completely apart. It's a bookkeeping choice, not a physical weirdness.
Only when the gravitational field is approximately uniform, meaning the height change is tiny compared to the planet's radius. For roller coasters and pendulums, mgh is fine. For satellites, orbits, and escape velocity, you must use U = -GMm/r.
No, they're negatives of each other: W_grav = -ΔU. When something falls, gravity does positive work while U decreases. Including both a gravity-work term and a ΔU term in one energy equation double-counts gravity and will cost you FRQ points.
Differentiate and flip the sign: F = -dU/dr. This is the calculus move that makes Physics C different from Physics 1, and it's how you check that differentiating U = -GMm/r gives back the inverse-square gravitational force.