Question

Discuss briefly about D’Alembert’s principle in plane motion of rigid body. What is significance of Principle of Work Energy in terms of stability of system, illustrate with an example.

Answer 1

D'Alembert showed that one can transform an accelerating rigid body into the same static system by adding the so-called "inertial force" and "inertial torque" or moment. The inertial force must act through the middle of mass and therefore the inertial torque can act anywhere. The system can then be analyzed exactly as a static system subjected to this "inertial force and moment" and the external forces.

Example of a rigid body in 1D:

To explain the concept of d'Alembert's principle, let’s use a simple model with a weight W, suspended from a wire. The weight is subjected to a gravitational force, W = mg, and a tension force T in the wire. The mass accelerates upward with an acceleration a. Newton’s Second Law becomes T – W = ma or T = W+ ma. As an observer with feet planted firmly on the ground. We see that the force T accelerates the weight, W, but, if we are moving with the wire we don’t see the acceleration, we feel it. The tension within the wire seems to counteract an acceleration “force” ma or (W/g) a