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.

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 

The mass moment of inertia is the product of moment of inertia and area. So L⁴ x L² = L⁶. so its unit will be m⁶.

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:

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

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

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

Polar moment of inertia of Solid cylinder:

Polar moment of inertia of Hollow Cylinder:

where outer diameter = D and inner diameter = d

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.

As the mass MOI is to be find along the y-axis, it would be Mb²/12.