Physics C: Mechanics · Unit 7: Gravitation · 14 min read · Updated 2026-05-11
Gravitational Forces — AP Physics C: Mechanics
AP Physics C: Mechanics · Unit 7: Gravitation · 14 min read
1. Newton’s Law of Universal Gravitation★★☆☆☆⏱ 3 min
Gravitational force is always attractive (there is no negative mass in classical mechanics, unlike electrostatic charge). By Newton’s third law, the force that mass 1 exerts on mass 2 is equal in magnitude and opposite in direction to the force mass 2 exerts on mass 1. This formula only applies directly to point masses and spherically symmetric extended masses; for non-spherical masses, we use superposition and integration.
Exam tip: On multiple-choice questions, use proportional reasoning ($F_g \propto m_1 m_2 / r^2$) to eliminate wrong options far faster than full numerical calculation.
2. Superposition of Gravitational Forces★★★☆☆⏱ 4 min
Gravitational force is a vector quantity, so when a test mass interacts with multiple source masses, the net gravitational force on the test mass is the vector sum of the individual forces exerted by each source. For AP problems, this process follows four steps:
Calculate the magnitude of each individual force using Newton’s law
Assign a coordinate system and resolve each force into $x$ and $y$ components
Add corresponding components to get net force components
Calculate the magnitude and direction of the net force if required
Exam tip: Always draw a coordinate system and confirm the direction of each force before adding components; AP examiners intentionally place masses to test sign errors for attractive forces.
3. Gravitational Force from Gravitational Field★★☆☆☆⏱ 3 min
Rearranging the definition gives the general relation between gravitational force and gravitational field: $\vec{F}_g = m \vec{g}$, where $m$ is the mass of the test object. The familiar near-Earth weight formula $F_g = mg$ is just an approximation of Newton’s universal law, valid only for points close to the surface. For any point outside a spherical mass $M$, the gravitational field magnitude is $g = \frac{GM}{r^2}$.
Exam tip: If asked for force at significant altitude above a planet’s surface, always calculate $g = GM/r^2$ instead of using the near-surface value of 9.8 m/s².
4. Extended Continuous Mass Distributions★★★★☆⏱ 4 min
For non-spherical continuous mass distributions, we use the principle of superposition with integration: we split the extended mass into infinitesimal mass elements, find the force from each element, then integrate over the entire distribution to get the net force. This is a common skill on AP Physics C Mechanics FRQs.
Common Pitfalls
Why: Students confuse the visible gap between objects with the separation required for the point-mass approximation.
Why: Students confuse force magnitude with resulting acceleration, assuming more mass creates more force.
Why: Students mix up gravitational force with electrostatic force, which can be repulsive, leading to reversed signs.
Why: Students memorize that spherical masses can be treated as point masses, so they incorrectly extend this to all shapes.
Why: When all forces are along one line, adding magnitudes with sign works, so students incorrectly extend this to 2D problems.