Test: Mass Moment of Inertia - Mechanical Engineering MCQ

The product of the mass and the square of the distance of the center of gravity of the mass from an axis is known as the mass moment of inertia about that axis.

As the mass MOI is to be find along the x-axis, it would be Md²/12.

The mass moment of inertia of circular plate is Mr²/4.

The mass MOI of a hollow circular cylinder is M(R + r)/4 where R is the outer diameter and r is the inner diameter.

The mass MOI of right circular cone of radius R and height H about its axis is 3MR²/10.

Moment of inertia of circular plate,


Moment of inertia of Square plate,


Calculation: The ratio of the moment of inertia of a circular plate to that of a square plate is, Which is less than 1.
Important Points
 The following table shows the Second moment of inertia of different shapes

Concept:
Moment of inertia of an area or Second moment of area (MI):

• MI of a body about any axis is defined as the summation of the second moment of all elementary areas about the axis.
• I = Σ(A × d²)

Unit: m⁴ or mm⁴ or cm⁴
For a square of side a or b:

Moment of inertia is 

Moment of inertia:
Moment of inertia is a measure of the resistance of a body to angular acceleration about a given axis that is equal to the sum of the products of each element of mass in the body and the square of the element’s distance from the axis.

Moment of inertia of a thin spherical shell of mass M and radius R about its diameter.
I = (2/3)MR²
Additional Information
Moment of inertia of some important shapes:

The moment of inertia (I₁) of a circular plate of diameter “D” is given by:

The moment of inertia (I₂) of the square plate of side equal to the diameter “D” of the circular plate is given by: