Rotational Dynamics — Definition Clarification What is the most precise definition of the mass moment of inertia (as used in dynamics)?

Introduction / Context:
The phrase “moment of inertia” is used in two nearby but distinct contexts: mass moment of inertia in dynamics and area moment of inertia in strength of materials. This question checks the exact definition relevant to rotational dynamics of bodies.

Given Data / Assumptions:

• We are talking about mass and rotation of rigid bodies (dynamics).
• Standard SI usage and definitions.

Concept / Approach:
The mass moment of inertia I about an axis is defined by integrating the squared distance of each mass element to that axis: I = ∫ r^2 dm. Because of the r^2 term, it is the second moment of the mass distribution.

Step-by-Step Solution:

Verification / Alternative check:
Contrast with strength of materials: area moment of inertia (second moment of area) I_z = ∫ y^2 dA is used in bending/deflection, not in rotational dynamics equations like T = I * α.

Why Other Options Are Wrong:
“Second moment of force” is not a standard concept; “Second moment of area” describes section properties, not kinetic rotational inertia; “All of these” mixes distinct quantities.

Common Pitfalls:
Using area properties in place of mass properties when computing kinetic energy, angular acceleration, or gyroscopic effects.

Final Answer:
Second moment of mass.