Home > List of equations in classical mechanics

1 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.

2 Defining Equations

2.1 Center of Mass

In the discrete case:

where 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.

2.2 Velocity

2.3 Acceleration

• Centripetal Acceleration

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

2.4 Momentum

2.5 Force

  (Constant Mass)

2.6 Impulse

  if F is constant

2.7 Moment of Intertia

For a single axis of rotation:

2.8 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

2.9 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

2.10 Precession

2.11 Energy

  if m is constant

  (near the earth's surface)

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

2.12 Central Force Motion

3 Useful derived equations

3.1 Position of an accelerating body

  if a is constant.

3.2 Equation for velocity