Circular Motion & Gravitation

AP Physics 1 • Unit 47-9.5%

Understanding motion along curved paths and the universal force of gravity. Learn why objects in circular motion accelerate even at constant speed, and how gravity governs planetary orbits.

Core Concepts

Centripetal acceleration – always toward the center
Centripetal force – the net force for circular motion
Period and frequency – describing rotation rate
Universal Gravitation – the inverse-square law
Gravitational field – g as a field quantity
Orbital motion – satellites and Kepler's laws with orbital conservation
Vertical circular motion – loops and varying tension/normal force

Key Equations

$a_c = \frac{v^2}{r} = \omega^2 r$

$F_c = \frac{mv^2}{r}$

$F = \frac{Gm_1 m_2}{r^2}$

$g = \frac{GM}{r^2}$

$T^2 = \frac{4\pi^2}{GM}r^3$

$v = \frac{2\pi r}{T}$

Real-World Applications

→Banked highway curves and with friction
→Satellite orbits and GPS
→Roller coaster loops and apparent weight
→Conical pendulum – circular motion with tension

Topic Map

🎯Where This Unit Leads

Master this material to build a strong foundation for these career paths.

Aerospace Engineering

Directly applies to orbital mechanics and satellite motion

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Mechanical Engineering

Rotating machinery and centrifuge design

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Physics

Gateway to gravitational physics and astrophysics

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