Derive an expression for moment of inertia about its tangent perpendicular to the plane.
The physical object is
made up of small particles. The Mass Moment of Inertia of the physical object
can be expressed as the sum of Products of the mass and square of its
perpendicular distance from the point which is fixed (A point which causes the
moment about the axis Passing thru it).
The Mass Moment of
Inertia can be Denoted by I
Les take a
consideration of a physical Body having a mass of m. This is composed of small
particles whose masses are m1, m2, m3,
…… etc. respectively. The perpendicular distance of each particle from the line
as shown figure are k1, k2, k3, …… etc.
From the above
statement, the Mass Moment of Inertia for the whole body can be written as
I = m1 (k1)2
+ m2 (k2)2 + m3 (k3)2 + ….. [eqn 1]
From the concept of
the centre of mass and centre of gravity, the mass of a body assumed to be
concentrated at on point.
The mass at that point
is m and The perpendicular distance of the point from the fixed line is k
∴hence m1 (k1)2 + m2 (k2)2 + m3 (k3)2
+ ….. = mk2 …….[eqn 2]
I =mk2
The physical object is made up of small particles. The Mass Moment of Inertia of the physical object can be expressed as the sum of Products of the mass and square of its perpendicular distance from the point which is fixed (A point which causes the moment about the axis Passing thru it).
The Mass Moment of Inertia can be Denoted by I
Les take a consideration of a physical Body having a mass of m. This is composed of small particles whose masses are m1, m2, m3, …… etc. respectively. The perpendicular distance of each particle from the line as shown figure are k1, k2, k3, …… etc.
From the above statement, the Mass Moment of Inertia for the whole body can be written as
I = m1 (k1)2 + m2 (k2)2 + m3 (k3)2 + ….. [eqn 1]
From the concept of the centre of mass and centre of gravity, the mass of a body assumed to be concentrated at on point.
The mass at that point is m and The perpendicular distance of the point from the fixed line is k
∴hence m1 (k1)2 + m2 (k2)2 + m3 (k3)2 + ….. = mk2 …….[eqn 2]
I =mk2
