# Tingkat kabébasan

(dipindahkeun ti Tingkat kabebasan)
Luncat ka: pituduh, sungsi

Frase "tingkat kebebasan" digunakeun dina 3 cabang elmu anu beda nyaeta: dina fisika jeung physical chemistry, dina mechanical jeung aeronautical engineering, sarta dina statistik. Tiluannana dihubungkeun sacara sajarah jeung ngaliwatan matematik nyaeta konsep 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 each 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 reached 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 least 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 area, or envelope) has six degrees of freedom. Three modes are translation - the ability to move in each of three dimensions. Three are rotation, or the ability to change angle around three perpendicular axes.

To put it in simpler terms, each of the following is one degree of freedom:

1. Moving up and down (heaving);
2. moving left and right (swaying);
3. moving forward and back (surging);
4. tilting up and down (pitching);
5. turning left and right (yawing);
6. tilting side to side (rolling).

See also: Euler angles.

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

## Statistik

Dina statistik, tingkat kabebasan nyaeta statistical parameter anu penting dina probability distribution. Contona dipake 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 dipake, tingkat kabebasan ngan nyokot integer (umumna kurang ti hiji). Sacara matematik diidinan keur ngabagi-bagi tingkat kabebasan, sahingga meunang hasil itungan nu nyugemakeun.

 Artikel ieu keur dikeureuyeuh, ditarjamahkeun tina basa Inggris. Bantosanna diantos kanggo narjamahkeun.