Question

Could you please provide an easy to follow explaination (not just copied and pasted from the internet) on the difference between the first moment of area and the second moment of area. I will leave feedback that reflects the quality of your response. Please no copying and pasting. Make the explaination east to understand, possibly with diagrams. Thank you.

Answer 1

The "second moment of area" is more commonly known as the "moment of inertia" and is a resistance to turning about an axis, just as inertia is resistance to movement.

The moment of inertia for a small particle is given by the mass of the particle multiplied by the square of the distance of the particle from the axis.

The moment of inertia for a large body is given by summing the moments of inertia for all particles of the body.

You know that the moment of force represents the magnitude of force applied to a rotational system at a distance from the axis of rotation

Moment = Force x Distance between the concerned point(or axis) and point of application of force
= Fr
You know that in case of self weight,
Force = Mass x 9.81 N= 9.81m

Also, mass = Density X Volume =pV



Hence,
Moment = Density X Volume X 9.81 X Distance
= 9.81pVr

The above is the first moment (i.e) Moment with respect to a point.

Second moment is with respect to an axis.

Hence, Moment = 9.81pVr^2

Now, Come to your question...

A)If the body considered is homogeneous, then density = constant.

If the body has a negligible third dimension, (Like a plate) Then thickness can be neglected .
Hence,
Moment of force
= 9.81pAtr = c Ar
The term AREA X DISTANCE (Ar) is called as First moment of area.

The first moment of area equals the summation of area times distance to an axis [Σ(a x r)]. It is a measure of the distribution of the area of a shape in relationship to an axis.
First moment of area is commonly used in engineering applications to determine the centroid of an object or the statical moment of area.

b) The second moment of area, also known as the area moment of inertia or second moment of inertia, is a property of a shape that is used to predict its resistance to bending and deflection which are directly proportional.

second moment of area= Ar^2