Class 11 Physics Kinetic Theory | Rotational Degree of freedom |

**Rotational Degree of freedom**

- Independent rotations that specify the orientation of a body or system.
- There is rotation of one part of the body with respect to the other part.

- Rotational degree of freedom happens only in diatomic gas.
- Diatomic molecules have rotational degrees of freedom in addition to translational degrees of freedom.
- It is possible in diatomic molecules as 2 atoms are connected together by a bond.So the rotation of one atomw.r.t to other atom.
- In diatomic there is translational in addition to that they have rotational degree of freedom also.
- For example: - Two oxygen atoms joined together by a bond. There are two perpendicular axes.
- There are 2 rotations possible along the two axes.
- They have 3 translational degrees of freedom and also 2 rotational degree of rotation.

- Therefore Rotational degree of freedom contributes a term to the energy that contains square of a rotational variable of motion.
- Rotational variable of motion comes from angular momentum ω.
- Linear velocity is v
_{x},v_{y},v_{z}. Whereas angular velocity is w_{x},w_{y},w_{z}. - E
_{R}(rotational) = (1/2)(I_{1}ω_{1})+(1/2)I_{2}ω_{2}. These are 3 rotationaldegrees of freedom along the 2 perpendicular axes.

- Linear velocity is v
- The total energy contribution due to the degrees of freedom for oxygen molecule.
- There will be 3 translational degree of freedom (1/2)m
_{x}v_{x}^{2},(1/2)m_{y}v_{y}^{2},(1/2)m_{z}v_{z}^{2}) - 2 rotational degree of freedom (1/2)I
_{1}^{2}ω_{1}^{2},(1/2)I_{2}^{2}ω_{2}^{2}

- There will be 3 translational degree of freedom (1/2)m

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