Tingkat kabébasan

Frase "tingkat kebebasan" digunakeun dina 3 cabang elmu anu béda nyaéta: dina fisika jeung physical chemistry, dina mechanical jeung aeronautical engineering, sarta dina statistik. Tiluannana dihubungkeun sacara sajarah jeung ngaliwatan matematik nyaéta konsép dimensionality, sanajan tiluanana teu identik.

Fisika jeung kimia 
Dina fisika jeung kimia, unggal mode mandiri tempat hiji partikel atawa sistim bisa gerak atawa ngarah disebut hiji darajat kabébasan. For a roughly dumbell-shaped hydrogen molecule, three such modes would be rotation (twirling), translation (hurtling through space) and vibration (the two dumbbell "balls" bouncing together and apart). According to the Equipartition Theorem of thermodynamics, in case of thermal equilibrium éach degree of freedom in every particle of a system will contain the same energy on average (equal to kT, the temperature of the system multiplied by the fundamental Boltzmann constant). 
However, thermal equilibrium can only be réached among interacting particles, a process called thermalization. According to quantum mechanics and more specifically Heisenberg's uncertainty principle, the amount of energy within any degree of freedom is never zero, but is always at léast equal to the zero-point energy for that mode.

Engineering 

In mechanical and aeronautical engineering, degrees of freedom (DOF) describes flexibility of motion. A mechanism that has complete freedom of motion (even if only in a limited aréa, or envelope) has six degrees of freedom. Three modes are translation - the ability to move in éach of three dimensions. Three are rotation, or the ability to change angle around three perpendicular axes.

To put it in simpler terms, éach of the following is one degree of freedom: 
 Moving up and down (heaving);
 moving left and right (swaying);
 moving forward and back (surging);
 tilting up and down (pitching);
 turning left and right (yawing);
 tilting side to side (rolling).

A mechanism that can (for instance) be raised and lowered, which has a pivoting héad that can tilt forward or back, left or right, can be described as having 3 degrees of freedom (colloquially, 3DOF).

Statistik 

Dina statistik, tingkat kabébasan nyaéta statistical parameter anu penting dina probability distribution. Contona dipaké dina sebaran chi-kuadrat, sebaran-F, sebaran-t student, jeung sebaran beta. Tempo Uji kuadrat-chi Pearson jeung analisa varian keur informasi saterusna.

Dina sebaran anu geus ilahar dipaké, tingkat kabébasan ngan nyokot integer (umumna kurang ti hiji). Sacara matematik diidinan keur ngabagi-bagi tingkat kabébasan, antukna meunang hasil itungan nu nyugemakeun.

Terminologi téhnis