This page gives a summary of important equations in classical mechanics. In physics, Classical mechanics is one of the two major sub-fields of study in the science of mechanics, which is concerned with the motions of bodies, and the forces that cause them. ...

Nomenclature

a = acceleration (m/s²)

g = gravitational constant (m/s²)

F = force (N = kg m/s²)

E_k = kinetic energy (J = kg m²/s²)

E_p = potential energy (J = kg m²/s²)

m = mass (kg)

p = momentum (kg m/s)

s = position (m)

R = radius (m)

t = time (s)

v = velocity (m/s)

v₀ = velocity at time t=0

W = work (J = kg m²/s²)

τ = torque (J = N m) (torque is the rotational form of force)

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 vecto

Velocity

Acceleration

• Centripetal Acceleration

(R = radius of the circle, ω = v/R angular velocity) Angular velocity describes the speed of rotation. ...

Momentum

Force

  (Constant Mass)

Impulse

  if F is constant

Moment of Inertia

For a single axis of rotation: The moment of inertia for an object is the sum of the products of the mass element and the square of their distances from the axis of rotation:

Angular Momentum

  if 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 - a tensor of rank-2) In mathematics, a tensor is a certain kind of geometrical entity, or alternatively generalized quantity. The tensor concept includes the ideas of scalars, vectors, and linear operators. ...

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

m is here constant.

in field of gravity

Central Force Motion

Useful derived equations

Position of an accelerating body

  if a is constant.

Equation for velocity