physics.center_of_mass¶

Calculating the center of mass for a discrete system of particles, given their positions and masses.

Description:

In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration.

Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualize its motion. In other words, the center of mass is the particle equivalent of a given object for the application of Newton’s laws of motion.

In the case of a system of particles P_i, i = 1, …, n , each with mass m_i that are located in space with coordinates r_i, i = 1, …, n , the coordinates R of the center of mass corresponds to:

R = (Σ(mi * ri) / Σ(mi))

Reference: https://en.wikipedia.org/wiki/Center_of_mass

Attributes¶

`Coord3D`
`Particle`

Functions¶

center_of_mass(→ Coord3D)

Input Parameters

Module Contents¶

physics.center_of_mass.center_of_mass(particles: list[Particle]) → Coord3D¶

Input Parameters¶

particles: list(Particle): A list of particles where each particle is a tuple with it’s (x, y, z) position and it’s mass.

Returns¶

Coord3D: A tuple with the coordinates of the center of mass (Xcm, Ycm, Zcm) rounded to two decimal places.

Examples¶

>>> center_of_mass([
...     Particle(1.5, 4, 3.4, 4),
...     Particle(5, 6.8, 7, 8.1),
...     Particle(9.4, 10.1, 11.6, 12)
... ])
Coord3D(x=6.61, y=7.98, z=8.69)

>>> center_of_mass([
...     Particle(1, 2, 3, 4),
...     Particle(5, 6, 7, 8),
...     Particle(9, 10, 11, 12)
... ])
Coord3D(x=6.33, y=7.33, z=8.33)

>>> center_of_mass([
...     Particle(1, 2, 3, -4),
...     Particle(5, 6, 7, 8),
...     Particle(9, 10, 11, 12)
... ])
Traceback (most recent call last):
    ...
ValueError: Mass of all particles must be greater than 0

>>> center_of_mass([
...     Particle(1, 2, 3, 0),
...     Particle(5, 6, 7, 8),
...     Particle(9, 10, 11, 12)
... ])
Traceback (most recent call last):
    ...
ValueError: Mass of all particles must be greater than 0

>>> center_of_mass([])
Traceback (most recent call last):
    ...
ValueError: No particles provided

physics.center_of_mass.Coord3D¶

physics.center_of_mass.Particle¶