What are degress of freedom?

Question

Can someone define degress of freedom for me please?

Answer 1

In mechanics, degrees of freedom (DOF) are the set of independent displacements that specify completely the displaced or deformed position of the body or system. This is a fundamental concept relating to systems of moving bodies in mechanical engineering, aeronautical engineering, robotics, structural engineering, etc.

A particle that moves in three dimensional space has three translational displacement components as DOFs, while a rigid body would have at most six DOFs including three rotations. Translation is the ability to move without rotating, while rotation is angular motion about some axis.

In statistical mechanics, a degree of freedom is a single scalar number describing the classical micro-state of a system. The micro-state of a system is completely described by the set of all values of all its degrees of freedom.

If the system studied can be described as a set of mechanical particles, then degrees of freedom are defined in the same manner as above. Thus, a micro-state of the system is a point in the system's phase space.

It must be noted that for a system, a micro-state defined by using degrees of freedom is intrinsically a classical state. This is because for a quantum micro-state, defining a precise value of both the position and momentum of a particle violates the Heisenberg uncertainty principle. The description of a system through a set of degrees of freedom is thus only valid in the classical (or high temperature) limit of statistical mechanics.

In some cases, when the system is not appropriately described as a set of mechanical particles, other types of degrees of freedom have to be defined. For example, in the 3D ideal chain model, two angles are necessary to describe each monomer's orientation. The value of each of these angles can each be a degree of freedom.

Answer 2

Degrees of freedom=n-1=11-1=10

Answer 3

Define Degress

Answer 4

In general, the degrees of freedom of a system is the number of variables necessary to describe the system. For example, a small beed moving on a wire has only 1 degree of freedom; a small beed moving on a plane has two degrees of freedom.