Definition : Degrees of freedom of a system the minimum number of independent coordinates needed to uniquely define the position or configuration of the system
Examples :
Single Particle in 3D Space : A single particle in three-dimensional space has 3 degrees of freedom. It can move independently in the x, y and z directions.
Rigid body in 3D Space : A rigid body has 6 degrees of freedom. Since it has 3 translational (movement along x, y and z axes) degrees of freedom and can rotate freely about three perpendicular axes, hence has 3 rotational degrees of freedom in addition.
Simple Pendulum : The bob of a simple pendulum has only one degree of freedom as it can only swing around a fixed point in a plane with fixed orientation in space. This degree of freedom is indicated by the angle θ of the deflection of the pendulum string from the normal from the support point.
Double Pendulum : A double pendulum consisting of two pendula connected in sequence, has 2 degrees of freedom. One degree of freedom corresponds to the angle of the first pendulum, and the second corresponds to the angle of the second pendulum relative to the first.
Diatomic Molecule : A diatomic molecule (like O₂) in a three-dimensional space has 5 degrees of freedom at room temperature: 3 translational (motion along x, y, and z axes) and 2 rotational (rotation about two perpendicular axes). The third rotation axis along the bond length is negligible for most diatomic gases due to quantum constraints.
