Unit Overview

Circular Motion and Gravitation Overview

AP Physics 1· 5 min read 📊 8-10% of total AP Physics 1 exam score

1. Unit at a Glance

We build this unit from the ground up: starting with the kinematics of circular motion, we explain why constant speed motion in a circle still requires non-zero acceleration. We then connect this acceleration to net force through Newton's second law, building a framework you can use to solve any circular motion problem.

After mastering terrestrial circular motion scenarios, we expand to gravitational interactions between masses, then connect gravitational force directly to the stable orbital motion of planets and satellites around larger bodies like the Sun or Earth.

This unit is split into 4 connected sub-topics:

AP Physics 1 Acceleration in Uniform Circular Motion

Defines centripetal acceleration, its magnitude, direction, and relationship to linear speed and radius.

★★⏱ 6 min

AP Physics 1 Force Analysis for Circular Motion

Teaches free-body diagram analysis to solve for net centripetal force in common circular motion scenarios.

★★★⏱ 8 min

AP Physics 1 Newton's Law of Universal Gravitation

Introduces the inverse square law of gravitation and how to calculate gravitational force between masses.

★★⏱ 5 min

AP Physics 1 Orbital Motion of Planets and Satellites

Applies circular motion and gravitation principles to analyze stable circular orbits.

★★★★⏱ 7 min

2. Common Pitfalls

Wrong move:

Treating centripetal force as an extra separate force that acts on objects in circular motion.

Why:

Centripetal force is just the net force pointing towards the center of the circle, not a new interaction force.

Correct move:

Sum all existing forces (tension, friction, gravity, normal) and set their center-point component equal to $m v^{2} / r$ .

Wrong move:

Confusing the universal gravitational constant $G$ with gravitational acceleration $g$ .

Why:

$G$ is a universal constant, while $g$ is a local acceleration that changes with distance from a massive body.

Correct move:

Remember $G = 6.67 \times 1 0^{- 11} Nm^{2} / kg^{2}$ , while $g \approx 9.8 m/s^{2}$ near Earth's surface.

3. Quick Reference Cheatsheet

Concept / Formula	Key Description
Centripetal Acceleration: $a_{c} = \frac{v ^{2}}{r} = ω^{2} r$	Magnitude of acceleration towards the center of a circular path
Centripetal Net Force: $F_{n e t, c} = \frac{m v ^{2}}{r}$	Newton's second law for the center-point direction of circular motion
Newton's Law of Gravitation: $F_{g} = G \frac{m _{1} m _{2}}{r ^{2}}$	Magnitude of gravitational force between two masses separated by distance $r$
Surface Gravitational Acceleration: $g = G \frac{M}{R ^{2}}$	Derives $g$ for the surface of a planet of mass $M$ and radius $R$
Stable Circular Orbit Speed: $v = \frac{GM}{r}$	Orbital speed required for a circular orbit of radius $r$ around mass $M$

What's Next

Begin this unit with the first sub-topic on acceleration in uniform circular motion to build the foundational kinematics you will need for all force analysis and gravitation problems. As you work through each sub-topic, connect new concepts to your existing knowledge of Newton's laws from earlier units. After completing this unit, you will move on to the next unit on work and energy.