AP Physics Chapter 9 Equations

R_A³ / T_A² = R_B³ / T_A²

R_A³ / T_A² = R_B³ / T_A²

Kepler’s 1st (Any Units)

R³ / T² = GM / 4𝝅²

Kepler’s 2nd (Standard Units ONLY; Meters, Seconds, Kgs)

R_A³  = T_A²

Keplers 3rd (AU’s and years ONLY; planets in OUR solar system)

F = GMm / d²

How to find the force of a planet

F_c = ma_c 

How to find centripetal force

Wr = V_T

How to find tangential velocity with radius and omega

M_ac = GMm / d²

How to find centripetal motion

a_c = V_T² / R

How to find centripetal acceleration

V_T = circumference / T

How to find tangential velocity

g = GM_planet / R_planet²

gravitational acceleration for ANY planet

V = d / t

How to find velocity

W = θ / t

How to find omega

1 cycle, 1 revolution, or 1 rotation = 2𝝅 radians = 2𝝅r

angular and linear conversions

Linear ÷ R = Angular

d, v, or a, to θ, Ꞷ, or 𝝰

Angular × R = Linear

θ, Ꞷ, or 𝝰, to d, v, or a,

d ⇌ θ

distance = theta

V ⇌ Ꞷ

velocity = omega

a ⇌ 𝝰

acceleration = alpha