AP Physics 1 Unit 3: Circular Motion & Gravitation
Study centripetal force, gravitational force, orbits, Kepler's laws with exam-format practice and rubric-based scoring.
Start AP Physics 1 Practice · Full Study Guide
AP and Advanced Placement are trademarks of College Board. AimFive is not affiliated with or endorsed by College Board.
Inside This Unit: The Full Breakdown
Circular Motion and Gravitation covers objects moving in circular paths and the universal force of gravity. This unit applies Newton's laws to situations where acceleration is directed toward the center of a circle.
Why it matters
Circular motion and gravity questions are common on the AP Physics 1 exam. You must understand centripetal acceleration, apply Newton's second law in the radial direction, and use Newton's law of gravitation. Satellite and orbital problems are frequently tested.
Key concepts
- Objects in uniform circular motion have constant speed but continuously changing velocity direction. Centripetal acceleration (ac = v²/r) points toward the center.
- Centripetal force is not a new type of force — it is the net inward force (gravity, tension, friction, normal force) that causes circular motion.
- Newton's law of universal gravitation: F = Gm₁m₂/r² describes the attractive force between any two masses.
- Orbital motion is free fall: the gravitational force provides the centripetal force needed for a circular orbit.
Uniform Circular Motion
An object moving in a circle at constant speed is undergoing uniform circular motion. Although its speed is constant, its velocity is continuously changing direction, which means the object is accelerating. This centripetal acceleration has magnitude ac = v²/r and always points toward the center of the circle. The period (T) is the time for one complete revolution, and speed relates to period by v = 2πr/T. By Newton's second law, a net force must cause this centripetal acceleration: ΣF = mac = mv²/r. This centripetal force is not a separate force — it is whatever real force (or combination of forces) points toward the center. For a car turning on a flat road, friction provides the centripetal force. For a ball on a string, tension provides it.
Newton's Law of Universal Gravitation
Every mass in the universe attracts every other mass with a gravitational force given by F = Gm₁m₂/r², where G = 6.67 × 10⁻¹¹ N·m²/kg² is the universal gravitational constant and r is the distance between the centers of the two masses. This force is always attractive, acts along the line connecting the two masses, and obeys Newton's third law (both objects experience equal and opposite forces). Near Earth's surface, this simplifies to F = mg, where g = GM_Earth/R_Earth² ≈ 9.8 m/s². Gravitational field strength (g = GM/r²) decreases with the square of the distance from a planet's center. This is why astronauts in orbit experience apparent weightlessness — they are in free fall, not beyond gravity's reach.
Orbital Motion and Satellites
Satellites in circular orbits are continuously falling toward the Earth but moving forward fast enough that the curved surface falls away at the same rate. The gravitational force provides the centripetal force: GMm/r² = mv²/r. Solving for orbital speed gives v = √(GM/r), which shows that closer orbits are faster. The orbital period can be found from T = 2πr/v. Kepler's third law (T² ∝ r³) follows directly from Newton's gravitation for circular orbits. Geostationary satellites orbit at a specific radius where T = 24 hours, allowing them to remain above the same point on Earth. These orbital mechanics problems require combining gravitational force with centripetal acceleration — a synthesis that appears frequently on the AP exam.
AP exam tip
On AP Physics 1, never list "centripetal force" as a force on a free-body diagram. Instead, identify the actual force providing the centripetal acceleration (gravity, tension, friction, normal force). Then set that force equal to mv²/r and solve.
Connections to other units
- Unit 2 (Dynamics): Circular motion is a direct application of Newton's second law with acceleration directed toward the center.
- Unit 4 (Energy): Gravitational potential energy (U = −GMm/r) and kinetic energy determine orbital characteristics.
- Unit 7 (Torque): Angular velocity and angular acceleration in rotational motion build on circular motion concepts.
