List of equations in classical mechanics

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)

s(t) = position at time t

s₀ = position at time t=0

r_unit = unit vector pointing from the origin in polar coordinates

θ_unit = unit vector pointing in the direction of increasing values of theta in polor coordinates

Note: All quantities in bold represent vectors.

Defining Equations

Center of Mass

In the discrete case:

Or in the continuous case:

Velocity

Acceleration

a_average = Δv/Δt

a = dv/dt = d²s/dt2

• Centripetal Acceleration

|a_c| = ω²R = v² / R

(R = radius of the circle, ω = v/R [angular velocity])

Momentum

p = mv

Force

∑F = dp/dt = d(mv)/dt

∑F = ma (Constant Mass)

Impulse

J = Δp = ∫Fdt

J = FΔt if F is constant

Moment of Intertia

For a single axis of rotation:

Angular Momentum

|L| = mvr iff v is perpendicular to r

Vector form:

L = r×p = Iω

(Note: I can be treated like a vector if it is diagonalized first, but it is actually a 3×3 matrix)

r is the radius vector

Torque

∑τ = dL/dt

∑τ = r×F

if |r| and the sine of the angle between r and p remains constant.

∑τ = Iα

This one is very limited, more added later. α = dω/dt

Precession

Energy

ΔKE = ∫F_net·ds

KE = ∫v·dp = 1/2 mv² if m is constant

PE_{due to gravity} = mgh (near the earth's surface)

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

Central Force Motion

Useful derived equations

Position of an accelerating body

s(t) = 1/2at² + v₀t + s₀ if a is constant.

Equation for velocity

v²=v₀² + 2a·Δs

Referenced By

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