Classical Mechanics/Equations

This page gives a summary of important equations in classical mechanics.

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Nomenclature

a = acceleration (m/s²)
F = force (N = kg m/s²)
KE = kinetic energy (J = kg m²/s²)
m = mass (kg)
p = momentum (kg m/s)
s = position (m)
t = time (s)
v = velocity (m/s)
v₀ = velocity at time t=0
W = work (J = kg m²/s²)
x(t) = position at time t
x₀ = position at time t=0

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Defining Equations

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Velocity

v = δs/δt = ds/dt

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Acceleration

a = δv/δt = dv/dt = d²s/dt²

Centripetal Acceleration

a_c = v² / R

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Momentum

p = mv

Angular Momentum

L = mvr

Vector form L = pxR

R is the radius vector

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Force

F = dp/dt = d(mv)/dt

F = ma (Constant Mass)

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Impulse

I = FΔt

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Energy

Kinetic Energy

KE = 1/2 mv²

Potential Energy

PE = mgh (near the earth's surface)

g is the acceleration due to gravity, one the physical constants.

Useful derived equations

Position of an accelerating body

x(t) = 1/2at² + v₀t + x₀

Equation for velocity
v²=v₀² + 2aΔx

where Δx is the change is position.

Someone please add the equations for gravitational, electric, and magnetic forces