Degrees of Freedom Values

Introduction to degrees of freedom:

The degrees of freedom of dynamical system are the number of independent coordinates required to specify completely the position and configuration of the system. Alternatively, the degrees of freedom of a dynamical system may be defined as the number of independent means by which the position and configuration of the system may be changed. Please try this What is the Unit for Force for solving your problems.


Explanation for degrees of freedom values


Find the values of degrees of freedom:

Suppose a particle is moving along a straight line. The position of the particle may be expressed completely by expressing its displacement along X-axis. Thus, a particle constrained to move along a straight line has one degree of freedom only.

If a particle is free to move in a plane, then its position may be specified by expressing X and Y-components of its displacement.It has two degrees of freedom values.

If a particle is free to move in space, then its position may be specified by expressing X, Y, Z components of its displacement vector. It has three degrees of freedom values.

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Degree of freedom values of different molecule's

Kinds of degrees of freedom values:

1. Degrees of freedom values of a rigid body:

A rigid body may perform translational and rotational motions. The translational motion is represented by centre of mass of body; which has three degrees of freedom values.The rotational motion of the body may also be resolved into three perpendicular components.So it also possesses three degrees of freedom.

2. Degrees of freedom of gas molecules:

Monoatomic gas: A molecule of a monoatomic gas like helium, neon, argon contains one atom only.

Translational kinetic energy = 1/2 mv2.

Its velocity has three components along perpendicular axes.Therefore a point mass has 3 degrees of freedom and there is no rotational motion.So the values of degrees of freedom  is 3 for monoatomic gas.

Diatomic gas: A molecule of diatomic gas has two atoms which are bound together by attractive forces.It has 2 types of motion:

Translational motion: The translational motion of molecule is represented by centre of mass, which has three degrees of freedom.

Rotational motion: The values of degrees of freedom is 5 that is it associated with diatomic molecule.

3. Triatomic gas: A molecule of a triatomic gas like linear triatomic molecule and non-linear triatomic molecule.

The linear triatomic molecule has degrees of freedom as 7. That is  f = 3n –l =3 x 3 -2 =7.

The non linear triatomic molecule has degrees of freedom as 6 that is f = 3n – l = 3 x 3 – 3 =6.

Kinetic Energy Increases

Kinetic Energy


Kinetic Energy

Many problems in physics require an application of kinetic energy. Kinetic energy is a form of energy that represents the

energy of motion. It is a scalar quantity, which means it has a magnitude but not a direction. It is, therefore, always

positive (as will be evident when we see the equation that defines it).
Deriving Kinetic Energy
Kinetic energy is closely linked with the concept of work, which is the scalar product (or dot product) of force and the.Is this topic Average Kinetic Energy hard for you? Watch out for my coming posts.

displacement vector over which the force is applied.
Using some basic kinematics equations, we obtain an equation for the acceleration of an object which changes speed. (In the

following equation, the term x - x0 has been replaced by s, a term which represents the total distance of displacement.)

v2 = v02 + 2as

therefore,

a = ( v2 - v02 ) / 2s

Applying Newton's Second Law of Motion, F = ma, we get:

F = ma = m ( v2 - v02 ) / 2s

and, multiplying by the distance s (for work) and breaking it apart, we get:

W = Fs = 0.5mv2 - 0.5mv02

The kinetic energy, K (or sometimes Ek) is, therefore, defined as:
K = 0.5mv2
It should be noted that, as mentioned before, this quantity will always be a non-zero scalar quantity. If the object has

mass and is moving, it will always be positive. It will be zero in the case of a massless object or an object at rest (zero

velocity). The kinetic energy equation, therefore, gives us no information about the direction of the motion, only about

the speed.
Work-Energy Theorem
The work-energy theorem comes from the above derivation, and indicates that the work done by an external force on a

particle is equal to the change in kinetic energy of the particle. Mathematically, then, you get:
Wtot = K2 - K1 = delta-K
Using Kinetic Energy
In addition to obtaining the work done, the kinetic energy equation is used frequently in conjunction with other forms of

energy. Due to the law of conservation of energy, we know that the total energy in a closed system will remain constant. Having problem with distance physics formula keep reading my upcoming posts, i will try to help you.

Therefore, analyzing the kinetic energy along with, say, gravitational potential energy allows us to figure out certain

factors of the motion.

End of Kinetic Energy