LAWS AND THEOREMS

Kennedy’s Theorem

If three plane bodies have relative motion among themselves, their I-centre must lie on a straight line.

Law Of Gearing

For constant angular velocity ratio of two gears, the common normal at the point of contact, of the two mating teeth must pass through the pitch point.

Zeroth Law Of Thermodynamics

When two systems are each in thermal equilibrium with a third system, then the two systems are also in thermal equilibrium with one another.

First Law Of Thermodynamics

O The heat and mechanical work are mutually convertible.

O The energy can neither be created nor destroyed though it can be transferred from one form to another.

Second Law Of Thermodynamics

According To Kelvin-Planck It is impossible to construct an engine working in a cyclic process, whose sole purpose is to convert heat energy from a single thermal reservoir into an equivalent amount of work.According To Clausius StatementIt is impossible for a self acting machine, working in a cyclic process, to transfer heat from a body at a lower temperature to a body at a higher temperature without aid of an external agency.

Boyle’s Law

The absolute pressure of a given mass of perfect gas varies inversely as its volume, when the temperature remains constant.

PV=constant

Charles’ Law

The volume of a given mass of perfect gas varies directly as its absolute temperature, when the absolute pressure remains constant.

V/T=constant

Gay-Lussac Law

The absolute pressure of a given mass of a perfect gas varies directly as its temperature, when the volume remains constant.

P/T=constant

Joule’s Law

The change of internal energy of a perfect gas is directly proportional to the change in temperature.

dE = mcdT

Newton’s First Law

Everybody continues in state of rest or of uniform motion in a straight line unless it is compelled by an external agency acting on it.

Newton’s Second Law

Rate of change of momentum of a body is directly proportional to the impressed force and it takes place in the direction of the force acting on it.

Newton’s Third Law

For every action there is an equal and opposite reaction.

Newton’s Law Of Gravitation

The force of attraction between any two bodies is directly proportional to their masses and inversely proportional to square of the distance between them.

Law Of Transmissibility Of Force

According to this law the state of rest or motion of the rigid body is unaltered if a force acting on the body is replaced by another force of same magnitude and direction but acting anywhere on the body along the line of action of the replaced force.

Triangle Law Of Forces

If two forces acting simultaneously on a body are represented by the sides of a triangle taken in order, their resultant is represented by the closing side of the triangle taken in the opposite order.

Parallelogram Law Of Forces

If two forces acting simultaneously on a body at a point are represented in magnitude and direction by the two adjacent sides of the parallelogram, their resultant is represented in magnitude and direction by the diagonal of the parallelogram which passes through the point of intersection of the two sides representing the forces.

Varignon’s Theorem

The algebric sum of the moments of a system of coplanar forces about a moment centre in their plane is equal to the moment of their resultant force about the same moment centre.

Lami’s Theorem

If a body is in equilibrium under the action of three forces, each force is proportional to sine of the angle between the other to forces.

Perpendicular Axis Theorem

The moment of inertia of an area about an axis perpendicular to its plane at any point is equal to the sum of moments of inertia about any two mutually perpendicular axis through the same point and lying in the plane of the area.

Parallel Axis Theorem

Moment of inertia about any axis in the plane of an area is equal to the sum of moment of inertia about a parallel centroidal axis and the product of area and square of the distance between the two parallel axis.

Hook’s Law

Stress is proportional to strain upto elastic limit,

Fourier’s Law Of Heat Conduction

The rate of flow of heat through a simple homogeneous solid is directly proportional to the area of the section at right angle to the direction of heat flow, and to change of temperature with respect to the length of the heat flow.

Wien’s Law

The wavelength corresponding to the maximum energy is inversely proportional to temperature of the body.

Kirchhoff’s Law

The emissivity of the body at a particular temperature is numerically equal to its absorptivity for radiant energy from body at the same temperature.

The Stefan-Boltzmann Law

The emissive power of black body is directly proportional to fourth power of its absolute temperature.

Lambert’s Cosine Law

Total emissive power from a radiating plane surface in any direction is directly proportional to the cosine of angle of emission.

Pascal’s LawPressure or intensity of pressure at a point in a static fluid is equal in all directions.