Difficulty: Easy
Correct Answer: True
Explanation:
Introduction / Context: Mass moment of inertia measures an object’s resistance to angular acceleration about an axis. Correct units are essential for dimensional consistency in torque and angular acceleration relationships.
Given Data / Assumptions:
Concept / Approach: The defining expression is I = ∫ r^2 dm for continuous bodies or I = Σ m_i r_i^2 for discrete masses. Thus, the dimension is [mass] * [length]^2, which in SI is kg·m^2.
Step-by-Step Solution:
Start with I = Σ m r^2. Replace m with kg and r with m, giving units kg·m^2. Check against rotational dynamics: τ = I * α has N·m on the left; α is rad/s^2 (dimensionless radians), leaving N·m = (kg·m^2) * (1/s^2), which is consistent since N = kg·m/s^2.Verification / Alternative check: For a solid disk, I = (1/2) m R^2; substituting SI units yields kg·m^2, confirming the unit again.
Why Other Options Are Wrong: 'False' would imply a different unit, contradicting dimensional analysis and standard definitions in mechanics.
Common Pitfalls: Confusing mass moment of inertia (kg·m^2) with area moment of inertia (m^4) used in beam bending; mixing CGS (g·cm^2) with SI (kg·m^2).
Final Answer: True.
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