List of equations in classical mechanics

This page gives a summary of important 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:

where n is the number of mass particles.

Or in the continuous case:

where ρ(s) is the scalar mass density as a function of the position vector.

Velocity

Acceleration

• Centripetal Acceleration

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

Momentum

Force

    (Constant Mass)

Impulse

 

    if F is constant

Moment of Intertia

For a single axis of rotation:

Angular Momentum

    iff v is perpendicular to r

Vector form:

(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

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

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

Precession

Energy

    if m is constant

    (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

    if a is constant.

Equation for velocity