4.
What is Moment of Inertia?
In physics, moment of inertia is a quantity expressing a
body's tendency to resist angular acceleration, which is the
sum of the products of the mass of each particle in the body
with the square of its distance from the axis of rotation.
Equation :
𝐼 = 𝑚 ∗ 𝑟2
m = Sum of the products of the mass
r = Distance from the axis of rotation
6.
What is Torque or Moment?
Torque, moment or moment of force, is the tendency of a
force to rotate an object about an axis.
What is Angular acceleration?
Angular acceleration is the rate of change of angular
velocity and is usually denoted by the Greek letter alpha
(α).
7.
Moment of Inertia
(Geometrical property of an area)
The moment of inertia of plane area or second moment
of inertia is a geometrical property of an area which
reflects how its points are distributed with regard to an
arbitrary axis.
8.
Area Moment of Inertia
The Area Moment Of Inertia of a beams cross-sectional
area measures the beams ability to resist bending. The
larger the Moment of Inertia the less the beam will
bend.
The moment of inertia is a geometrical property of a
beam and depends on a reference axis. The smallest
Moment of Inertia about any axis passes through the
centroid.
9.
𝐼 𝑥=
𝑦 2 𝑑𝐴
𝐼 𝑦=
𝑥 2 𝑑𝐴
y is the distance from the x axis to an area dA
x is the distance from the y axis to an area dA
10.
Polar Moment Of Inertia
Moment of Inertia about the z axis
The Polar Area Moment Of Inertia of a beams
cross-sectional area measures the beams ability
to resist torsion. The larger the Polar Moment of
Inertia the less the beam will twist.
11.
𝐼 𝑧 = (𝑥 2 +𝑦 2 ) dA
y is the distance from the x axis to an area dA
x is the distance from the y axis to an area dA
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