Body Force vs Inertial Force: What's the Difference?

[CamJPete]

Hello everyone. This is my first time on the physics forum, but I think I'm going to be a regular here.

I was reading a paper that outlined various ways to approach solving dynamic problems. The first approach outlined by the author is D'Alembert's principle of virtual work. In describing the history of this method, he states that "The technical community eventually took the position that dynamics should not be treated as a special case of statics, but rather the other way around. In other words, we soon placed the ma term on the right side of the equations of motion and included only real (contact and body) forces on the left side."(underlines added)

I understand what he is saying here that this principle eventually morphed into Newton's second law of F=ma, but I am confused by his calling a body force a "real" force. As I currently understand it, the m*a term is called an "inertial or psuedo force" (caused by resistance to motion, not truly a real force). But isn't the body force (say due to acceleration of gravity acting on the mass) an inertial force also? Why would it be included on the left side? In short: "what is the difference between a body force due to gravitational acceleration (that apparently belongs as part of sum of F on the left side of the equation), and an inertial force due to acceleration (that apparently belongs on m*a right hand side of the equation)?

 

[Dr.D]

As used in that statement, the term "body force" is intended to describe such things a gravitational force or a buoyant force. The essential character of a "body force" is that it is distributed over a body, or at least over an exterior surface. A contact force acts at an identifiable point, such as a point of attachment.

 

[Dale]

But isn't the body force (say due to acceleration of gravity acting on the mass) an inertial force also?

This is a good question, but it doesn't have a good answer. The answer is "it depends".

In Newtonian mechanics the force of gravity is taken to be a real force which acts on the whole body (hence a body force). Although it is proportional to mass like an inertial force, it is considered to be a real force by virtue of the fact that it comes in 3rd law pairs unlike inertial forces.

In General Relativity, the answer is different, the force of gravity is taken to be an inertial force. All forces which are proportional to mass and therefore are undetectable by an accelerometer are treated as inertial forces, and only forces which cause detectable acceleration by an attached accelerometer are considered to be real forces.