Physics equations

𝝆

m/V

v_avg

(Δx)/(Δt)

speed_avg

(Δx_total)/(Δt)

slope

x/y

v

(dx)/(dt)

a_avg

(ᐃv)/(ᐃt)

a

(dv)/(dt)

a

(d²x)/(dt²)

a

-g

a^→ x b^→

(a_yb_z - b_ya_z)i + (a_zb_x - b_za_x)j

a^→ x b^→

(a_xb_y - b_xa_y)k

r^→

xî+yĵ+zk̂

v^→_avg

(Δr^→)/(Δt)

v^→

(dr^→)/(dt)

v_ox

v_ocos𝜃_o

v_oy

v_osin𝜃_o

R

((vcosθ)/g)((vsinθ)+sqrt((v²sin²θ)+2gy₀))

T

(2𝝅r)/v

When two frames of reference A and B are moving relative to each other at constant velocity:

v^→_PA

v^→_PB + v^→_BA

When two frames of reference A and B are moving relative to each other at constant velocity:

a^→_PA

a^→_PB

F^→_net

ma^→

W^→

mg^→

F^→_BC

-F^→_CB

Drag force for air:

D

.5CρAv²

F_c

mv²/R

F_net

F⁺ - F^-

Banked turn without friction:

𝝧

tan^-1((v²)/(gR))

W

Fdcos𝛉

W

F·d

W_net

ΔK

W_s

(1/2)kx_i² - (1/2)kx_f²

W

m∫vdv

Area of a trapezoid:

A

(1/2)(a + b)(h)

P

Fvcosθ

ΔU

-W

U_g

mgh

E_mec

K + U

W

ΔE_mec +  ΔE_th +  ΔE_int

E_th

F_fd

P

(dE)/(dt)

K₁+ U₁ + U_s1

K₂+ U₂+ U_s2+ W_f

x_com

(m₁x₁+ m₂x₂)/(m₁+ m₂)

When the force is constant:

J^→

FΔt

P_i

P_f

ϴ

s/r

ω_avg

(Δϴ)/(Δt)

𝜶_avg

(Δω)/(Δt)

ϴ - ϴ₀

(1/2)(ω₀ + ω)t

x - x₀

(1/2)(v₀ + v)t

s

ϴr

T

(2𝛑r)/v

a_r

v²/r

a_r

ω²r

𝜏

rFsinθ

𝜏_net

I𝜶

P

𝞃ω

v_com

(ds)/(dt)

For smooth rolling motion:

v_com

ωR

When the axis of rotation is the point where the wheel touches the ground:

v_top

2(ωR)

When the axis of rotation is the point where the wheel touches the ground:

v_top

2v_com

I_P

I_com + MR²

If the wheel does not slide:

F

F_s

If the wheel slides:

F

F_k

When rolling down a ramp without sliding:

a_com

(-gsin𝝷)/(1 + I_com/MR²)

L^→

r^→p^→sinθ

𝜏_net

(dL)/(dt)

If there is no net external torque:

L_i

L_f

g_planet

GM_planet/R²_planet

v

(GM/R)^1/2

E

-GmM/(2(semi-major axis))

v_e

((2GM)/R)^1/2

(dA)/(dt)

(1/2)r²𝜔

(dA)/(dt)

L/(2m)

GmM/(semi-major axis)²

mv²/(semi-major axis)

GmM/(semi-major axis)²

m𝜔²(semi-major axis)

T²

(4𝝿²/GM)(semi-major axis)³

R_a + R_p

2(semi-major axis)

K_G

(GMm)/(2(semi-major axis))

K_G

-U_G/2

E_G

-K_G

E_G

-(GMm)/(2(semi-major axis))

v

-⍵x_maxsin(⍵t + 𝜙)

a

⍵²x_maxcos(⍵t + 𝜙)

a

⍵²x

F

-m⍵²x

k

m⍵²

⍵

(k/m)^1/2

U_s

(1/2)kx_max²cos²(𝜔t + 𝜙)

K

(½)m𝜔²sin²(𝜔t + 𝜙)

E

(1/2)kx_max²

I

∑mr²

I/mgh

𝓁/g

Physical pendulum:

g

(8𝜋²L)/(3T²)