The inertia force \(\mathbf{F}_{in}\) introduced in D'Alembert's principle for a rigid body with center of mass acceleration \(\mathbf{a}_C\) and mass \(m\) is:

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Mechanical Engineering QUESTION #2480

Question 1

\(\mathbf{F}_{in} = m\mathbf{a}_C\)
\(\mathbf{F}_{in} = -I_C\boldsymbol{\alpha}\)
\(\mathbf{F}_{in} = -m\mathbf{a}_C\)✔️
\(\mathbf{F}_{in} = m\mathbf{g}\)

Correct Answer Explanation

D'Alembert's principle introduces the inertia force \(\mathbf{F}_{in}=-m\mathbf{a}_C\) and inertia moment \(M_{in}=-I_C\alpha\). Adding these fictitious terms to real external forces converts the dynamic problem into an equivalent static equilibrium.

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