Units check – mass moment of inertia Choose the correct SI-style units for the mass moment of inertia of a rigid body about an axis.

Introduction / Context:
Mass moment of inertia quantifies a body’s resistance to angular acceleration about a given axis. Correct units matter for validating formulas, checking finite element outputs, and converting catalog data for rotors, gears, and flywheels.

Given Data / Assumptions:

• Using SI base units: mass in kg, length in m, time in s.
• Mass moment of inertia I relates to torque and angular acceleration via τ = I * α.
• We distinguish mass moment of inertia from area moment of inertia used in beam bending.

Concept / Approach:

From τ = I * α and dimensional analysis: [τ] = N·m = kg·m^2/s^2 and [α] = 1/s^2. Therefore [I] = [τ]/[α] = (kg·m^2/s^2) / (1/s^2) = kg·m^2. This matches the integral definition I = ∫ r^2 dm, where r has units of meters and dm has units of kilograms, producing kg·m^2.

Step-by-Step Solution:

Verification / Alternative check:

Integral form: I = ∫ r^2 dm → units r^2 (m^2) times dm (kg) gives kg·m^2 directly.

Why Other Options Are Wrong:

(a) and (b) involve division by meters; incorrect. (c) m^4 is the area moment of inertia unit, not mass moment. (d) m^3 is a volume unit.

Common Pitfalls:

Confusing mass moment of inertia (kg·m^2) with second moment of area (m^4); mixing torque with energy units.

Final Answer:

kg·m^2