Triangular law and parallelogram law of addition

What is the use of triangular & parallelogram law?

Now, we know that adding scalar quantities is very simple, just we need to add it normally but for vector quantities such as force, we cannot perform addition like this. So, to add the vector quantity we use the triangular law and parallelogram law. 

Remember that this two law can be used only for the addition of 2 force or 2 vector quantity.

Triangular law for addition: 

If two forces acting simultaneously on a body such that they can be represented by two adjacent sides of a triangle taken in same order, then their resultant will be equal to the third closing side of triangle taken in opposite direction or order.

Parallelogram law for addition:

If two vectors are represented by two adjacent sides of parallelogram then the diagonal through intersection represents their resultant.


These are the graphical method to add vector. we can also use analytical method for the addition of vector.

Scalar, vector and tensor quantity

What is scalar quantity, vector quantity & tensor quantity?

To define any scalar quantity we required only magnitude of that quantity. So, those quantity which can be fully defined based on their magnitude only are scalar quantities. eg. Time, volume, speed etc.

To define any vector quantity we required  magnitude as well as direction of that quantity. So, those quantity which can be fully defined based on their magnitude and direction are vector quantities. By knowing only the magnitude of it, it cannot be fully defined. eg. velocity, acceleration etc.

To define a tensor quantity we required magnitude, direction and the area or plane on which it is acting. So those quantity which can be fully defined only by knowing all three of these are tensor quantity. eg. Stress on a material

Dyne

What is dyne?

It is the force required to accelerate a mass of one gram at a rate of one centimeter per second squared.

1 Dyne = 1 g.cm/s^2 = 10^-5 N

Newton

What is newton?

A newton is how much force is required to make a mass of one kilogram accelerate at the rate of one meter per second square.

1N = 10^5 Dyne

1N = 1kg.m/s^2

Force

What is force?

It is the push or pull which create or tends to create motion, destroy motion or tends to destroy motion.

Force is a vector quantity.

Unit of force in SI system is Newton,
Unit of force in CGS system is Dyne.

Note: 1 N = 10^5 Dyne

Engineering Mechanics

Engineering mechanics is sub-divided into two parts:

1) Static
2) Dynamic

Here, statics deals with stationary bodies where as dynamic deals with the body in motion.

Further, dynamic can be subdivided into kinematics and kinetics.

Kinematics deals only with motion of the body and not the forces causing them where as Kinetics deals with both motion of the body and the forces causing them.

Classification of Mechanics

Engineering Mechanic can be classified as:

1) Engineering Mechanics

2) Strength of materials

3) Mechanics of fluids

Engineering mechanics deals with the rigid bodies or external force acting on the body.

Strength of material deals with the deformable bodies or internal forces acting on the bodies.

Mechanics of fluid deals with the compressible and in compressible fluid i.e. gases or liquids.