Which one of the following principles states that the inertia forces and couples, and external forces and torques on a body together give statical equilibrium?

Explanation:

D' Alembert principle:

• D'Alembert's principle of virtual work states that a system of rigid bodies is in dynamic equilibrium when the virtual work of the sum of the applied forces and inertial forces is zero for any virtual displacement of the system.

​Equation of motion is given by:

F = m × a

It can be rearranged as:

F + (- m × a) = 0 (As per D'Alembert"s principle)

• It tends to give the solution procedure of a dynamic problem an appearance akin to that of a static problem.
• D’Alembert demonstrated that by adding inertial force, inertial torque or moment, and external forces and torques, an accelerating rigid body can be transformed into an equal static system.
• The inertial torque can act anywhere and the inertial force must act through the centre of mass.
• The system can therefore be evaluated as a static system that is subjected to the inertial force and moment as well as external forces.
• The advantage is that one can take moments about any position in the comparable static system (not just the centre of mass) because each force (in turn) can be eliminated from the moment equations by finding the right point about which to apply the moment equation (sum of moments = zero), this typically leads to simplified computations.
• This principle is used to analyze the forces that act on a link of a mechanism while it is in motion in Fundamentals of Dynamics and Kinematics of Machines.