The ____ expresses the relation between the external forces applied to a system of particles and the effective force on each particle of the system.

The ____ expresses the relation between the external forces applied to a system of particles and the effective force on each particle of the system.

• A. Inertia force of particle
• B. D'Alembert's principle
• C. Newton's Law of Motion
• D. None of the above

Answer: (B)

This question tests how dynamics of a system of particles can be recast as a static balance by including inertial effects. D'Alembert's principle says that for any admissible virtual displacement of the particles, the sum over all particles of (external forces minus inertial forces) dotted with the virtual displacement is zero. In formulas, the effective force on each particle is F_ext,i − m_i a_i, and the principle states that the total virtual work of these effective forces is zero: sum_i (F_ext,i − m_i a_i) · δr_i = 0 for all allowed δr_i. This makes the dynamic problem resemble a static equilibrium problem and is especially useful when constraints tie the particles together. So the statement is capturing that idea: the external forces together with the inertial (m_i a_i) terms define an effective force on each particle, and their balance in the virtual-work sense expresses the motion of the system. Inertia alone is just the inertial term and does not by itself relate external forces to motion; Newton's law F = m a describes the relation for a single particle but does not encode the system-wide, constraint-based balance that D'Alembert's principle provides. None of the above is not correct because this principle precisely expresses that relationship.

This question tests how dynamics of a system of particles can be recast as a static balance by including inertial effects. D'Alembert's principle says that for any admissible virtual displacement of the particles, the sum over all particles of (external forces minus inertial forces) dotted with the virtual displacement is zero. In formulas, the effective force on each particle is F_ext,i − m_i a_i, and the principle states that the total virtual work of these effective forces is zero: sum_i (F_ext,i − m_i a_i) · δr_i = 0 for all allowed δr_i. This makes the dynamic problem resemble a static equilibrium problem and is especially useful when constraints tie the particles together.

So the statement is capturing that idea: the external forces together with the inertial (m_i a_i) terms define an effective force on each particle, and their balance in the virtual-work sense expresses the motion of the system. Inertia alone is just the inertial term and does not by itself relate external forces to motion; Newton's law F = m a describes the relation for a single particle but does not encode the system-wide, constraint-based balance that D'Alembert's principle provides. None of the above is not correct because this principle precisely expresses that relationship.