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.
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
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