AP Physics 1 Equations

A full list of the Algebra-Based AP Physics 1 Equations

Sorted by Chapters

Check out the Appendix of Variables for all the variables used in the AP Physics Classes

Kinematic Equations
1.	$V_{f}$ = Final Velocity $V_{i}$ = Initial Velocity $a$ = Acceleration $t$ = Time	$V_{f} = a t + V_{i}$
2.	$ΔX$ = Displacement $V_{i}$ = Initial Velocity $a$ = Acceleration $t$ = Time	$ΔX = \frac{1}{2} a t^{2} + V_{i} t$
3.	$ΔX$ = Displacement $V_{f}$ = Final Velocity $V_{i}$ = Initial Velocity $a$ = Acceleration	${V_{f}}^{2} = {V_{f}}^{2} + 2 a ΔX$
4.	$ΔX$ = Displacement $V_{f}$ = Final Velocity $V_{i}$ = Initial Velocity $t$ = Time	$ΔX = \frac{V_{i} + V_{f}}{2} \times t$

Dynamics Equations
Newton's Second Law	$\sum F$ = Net Force $m$ = Mass $a$ = Acceleration	$\sum F = m a$
Force of Kinetic Friction	$F$ = Force $μ$ = Coefficient of Friction $F_{n}$ = Normal Force	$F_{k} = μ_{k} F_{n}$
Force of Static Friction	$F$ = Force $μ$ = Coefficient of Friction $F_{n}$ = Normal Force	$F_{s} \leq μ_{s} F_{n}$

Circular Motion and Gravitational Equations
Gravitational Force	$F_{g}$ = Gravitational Force $m$ = Masses $G$ = $6.67 \times 10^{-11}$ $m^{3} / kg s^{2}$ $r$ = Center-to-Center Distance	$F_{g} = G \frac{m_{1} m_{2}}{r^{2}}$
Gravitational Field Strength	$F_{g}$ = Gravitational Force $m$ = Mass	$g = \frac{F_{g}}{m}$

Energy Equations
Work	$W$ = Work $F_{∥}$ = Force parallel to the Direction of Motion $d$ = Distance	$W = F_{∥} d$
Kinetic Energy	$K$ = Kinetic Energy $v$ = Velocity $m$ = Mass	$K = \frac{1}{2} m v^{2}$
Gravitational Potential Energy	${ΔU}_{g}$ = Gravitational Potential Energy $m$ = Mass $g$ = Acceleration due to Gravity $h$ = Height	${ΔU}_{g} = m g h$
Gravitational Potential Energy	$U_{G}$ = Gravitational Potential Energy $m$ = Masses $G$ = $6.67 \times 10^{-11}$ $m^{3} / kg s^{2}$ $r$ = Center-to-Center Distance	$U_{G} = G \frac{m_{1} m_{2}}{r}$
Elastic Potential Energy	$U_{s}$ = Elastic Potential Energy $k$ = Spring Constant $x$ = Displacement	$U_{s} = \frac{1}{2} k x^{2}$
Rotational Energy	$K_{r}$ = Rotational Energy $I$ = Rotational Inertia $ω$ = Angular Speed	$K_{r} = \frac{1}{2} I ω^{2}$
Power	$P$ = Power $W$ = Work $t$ = Time	$P = \frac{W}{Δt}$

Momentum Equations
Momentum	$p$ = Momentum $m$ = Mass $v$ = Velocity	$p = m v$
Impulse	$J$ = Impulse $F$ = Force $t$ = Time	$Δp = J = F Δt$

Simple Harmonic Motion Equations
Hooke's Law	$F_{s}$ = Spring Force $k$ = Spring Constant $x$ = Displacement	$F_{s} = k x$
Period of an Oscillating Spring	$T$ = Period $m$ = Mass $k$ = Spring Constant	$T_{s} = 2 π \sqrt{\frac{m}{k}}$
Period of a Swinging Pendulum	$T$ = Period $l$ = Length of Pendulum $g$ = Acceleration due to Gravity	$T_{p} = 2 π \sqrt{\frac{l}{g}}$
Position of a Mass on an Oscillating Spring	$x$ = Position $A$ = Amplitude $ω$ = Angular Speed $t$ = Time	$x = A \sin (ω t)$

Torque and Rotational Motion
1. Angular Kinematic Equation	$θ$ = Angular Displacement $ω_{i}$ = Initial Angular Speed $α$ = Angular Acceleration $t$ = Time	$θ = \frac{1}{2} α t^{2} + ω_{i} t$
2. Angular Kinematic Equation	$ω_{f}$ = Final Angular Speed $ω_{i}$ = Initial Angular Speed $α$ = Angular Acceleration $t$ = Time	$ω_{f} = α t + ω_{i}$
3. Angular Kinematic Equation	$ω_{f}$ = Final Angular Speed $ω_{i}$ = Initial Angular Speed $α$ = Angular Acceleration $θ$ = Angular Displacement	${ω_{f}}^{2} = {ω_{f}}^{2} + 2 α θ$
Centripetal Acceleration	$a_{c}$ = Centripetal Acceleration $v$ = Velocity $r$ = Radius	$a_{c} = \frac{v^{2}}{r}$
Torque	$τ$ = Torque $r_{⊥}$ = Radius perpendicular to the Force $F$ = Force	$τ = r_{⊥} F$
Angular Acceleration	$α$ = Angular Acceleration $\sum τ$ = Net Torque $I$ = Rotational Inertia	$α = \frac{\sum τ}{I}$
Angular Momentum	$L$ = Angular Momentum $I$ = Rotational Inertia $ω$ = Angular Speed	$L = I ω$
Angular Impulse	$ΔL$ = Angular Impulse $τ$ = Torque $t$ = Time	$ΔL = τ Δt$