# Formulae

Below are the formulae that are listed on the classroom walls.

They are in no particular order and are updated regularly.

If one is missing, please notify your beloved teacher.

All the formulae listed below may be used on any test.

S=d/t

V_{av} = ∆x/∆t

V_{AC} = V_{AB} + V_{BC}

A =∆v/∆t

V_{f} = V_{i} + at

∆x = V_{i}t + (1/2)at^{2}

V_{f}^{2} = V_{i}^{2} + 2a∆x

V_{x} = Vcosθ

V_{y} = Vsinθ

∆x = V_{x}t

∆y = V_{y}t + (1/2)gt^{2}

∆y = (tanθ)∆x + (g∆x^{2})/(2V^{2}cos2θ)

∆x = -(V^{2}sin2θ)/g lands at same level

θ = arc length/radius (in radians)

ω_{f} = ω_{i} +αt

∆θ = ωit + (1/2)αt2

ω_{f}^{2} = ω_{i}^{2} + 2α∆θ

∆θr = d

ωr = v_{t}

αr = a_{t}

ω = ∆θ/∆t

α = ∆ω/∆t

1 radian = (arc length of r)/r

T = (1/2)mv^{2}

∆U = -mgh

H = mc∆T

1 J = 1 kg.m^{2}/sec^{2}

H = mh_{f} or mh_{v}

ΣF = ma

W = mg

∆U_{sp} = (1/2)k∆x^{2}

Eff = out/in = (total energy – ∆E)/(total energy)

FΔt = mΔv

Δp = Δmv

FΔt = Δp

Δp = 0 (cons of momentum)

V_{1f}/V_{1i} = (m_{1}-m_{2})/(m_{1}+m_{2})

V_{2f}/V_{1i} = 2m_{1}/(m_{1}+m_{2})

ΣF = ma, ΣF = 0

ΣF_{x}=0, ΣF_{y}=0

F_{f} = μN

A_{c} = v_{t}^{2}/r

F_{c} = mv_{t}^{2}/r

ΣF_{r} = mv_{t}^{2}/r, ΣF_{θ}=0

V^{2} = μgr

V^{2} = rgtanθ

ΣT = 0

T = Fd┴ = F┴d

∑T = Iα

T_{rot} = (1/2)Iω^{2}

L = mvr = Iω

∆L = 0

ω = 2πν

ω = 2π/T

T = 1/ν

ν = 1/T

x(t) = X_{max}cos(ωt + Φ)

v(t) = ώX_{max}sin(ωt + Φ)

a(t) = ώ2X_{max}cos(ωt + Φ)

v_{max} = ωX_{max}

a = ω2X_{max}

T^{2} = 4π2L/g

W = Fd║ = Fdcosθ

W = ΔT = ΔE

T_{i} = T_{f} + ΔU + ΔH + ΔE_{d}

F = -Gm_{1}m_{2}/r^{2}

g_{1} = F_{12}/m_{2} = -Gm_{1}/r^{2}

ΔU_{r∞} = -Gm_{1}m_{2}/r

ΔU_{AB} = ΔU_{A∞} + ΔU_{∞B} = ΔU_{A∞} - ΔU_{B∞}