date: Nov 20, 2020.
We discuss Newton's definition of inertia. It can be found on page 12 of the book Newton's Philosophy of Nature. The passage is broken down sentence by sentence.
This is the full quote:
The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, continues in its present state, whether it be of rest or of moving uniformly forward in a right line.
This force is always proportional to the body whose force it is and differs nothing from the inactivity of the mass, but in our manner of conceiving it. A body, from the inert nature of matter, is not without difficulty put out of its state of rest or motion. Upon which account, this vis insita may, by a most significant name, be called 'inertia' (vis inertiae) or 'force of inactivity'. But a body only exerts this force when another force, impressed upon it, endeavors to change its condition; and the exercise of this force may be considered as both resistance and impulse; it is resistance so far as the body, for maintaining its present state, opposes the force impressed; it is impulse so far as the body, by not easily giving way to the impressed force of another, endeavors to change the state of that other. Resistance is usually ascribed to bodies at rest, and impulse to those in motion; but motion and rest, as commonly conceived, are only relatively distinguished; nor are those bodies always truly at rest which commonly are taken to be so.
The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, continues in its present state, whether it be of rest or of moving uniformly forward in a right line.
This is a summarised definition of inertia. Newton mentions bodies that are not moving ("at rest") and those traveling straight ("in a right line") with unchanging speed ("moving uniformly"). He describes the property of inertia as the tendency of objects in general, to want to remain in either of those states. That is to say, objects that are not being acted upon by an outside force exist in either of these two states and, in particular, when forces do act upon them, they resist changing that state.
Now, in the case of static objects, our commonplace experience shows that they are in fact still until we move them. For instance, an object sitting on a table does not move of its own, unless we make it move. In that example, we act as the outside force. However, in the case of an object moving uniformly in a straight line, our usual experience is that it stops naturally (A flying object like a baseball eventually falls to the ground). Well, Newton is saying that objects that move continually in a straight line keep that way unless something acts upon them. If we analyze the baseball, there are actually a couple of main forces acting upon it. There is a downward pull caused by Earth's gravity, and there is a resistance caused by the air. If gravity were not present, the ball would continue in an upward trajectory into space. If air resistance were not present, it would travel forward with the speed of the initial bat hit, indefinitely.
But then, what is inertia? Let us imagine a heavier baseball. Then, gravity will need to exert a larger force upon it to make it drop. Also, the air resistance will need to be greater to cause an equivalent slowdown. Basically, the heavier the flying object, the tougher it becomes to affect its original state of motion, the more resistance it has to changing it. Inertia is that resistance, characteristic of all objects. We can see that heavy objects possess more inertia than light objects.
This force is always proportional to the body whose force it is and differs nothing from the inactivity of the mass, but in our manner of conceiving it.
Here, when Newton says this force, he means inertia. An object's inertia is itself a force against other objects, since it opposes their action. He then says it is indistinguishable from, or is the same as, the object not doing anything. But that there is ambiguity in how we interpret the phenomenon. This is explained toward the end of the paragraph.
A body, from the inert nature of matter, is not without difficulty put out of its state of rest or motion.
Recapitulating, objects have inherent resistance to changing their natural motion, called inertia.
Upon which account, this vis insita may, by a most significant name, be called 'inertia' (vis inertiae) or 'force of inactivity'.
He names this observed property of objects inertia.
But a body only exerts this force when another force, impressed upon it, endeavours to change its condition; and the exercise of this force may be considered as both resistance and impulse; it is resistance so far as the body, for maintaining its present state, opposes the force impressed; it is impulse so far as the body, by not easily giving way to the impressed force of another, endeavours to change the state of that other.
As mentioned previously, our interpretation of inertia can vary. If some force acts upon an object, from the perspective of the object under consideration, it is resisting change due to that force. But, if, say, the force is coming from a second object, from that object's point of view, the first object is wanting to change its motion. This is, again, why inertia is simultaneously a resistance, and a force.
Resistance is usually ascribed to bodies at rest, and impulse to those in motion; but motion and rest, as commonly conceived, are only relatively distinguished; nor are those bodies always truly at rest which commonly are taken to be so.
Here, Newton is referring to objects at rest and those moving with unchanging speed, and he is saying that they are actually two sides of the same coin. Take a plane flying across the sky. From our perspective, the plane is moving (with some set speed) but we are not. But from the perspective of the people inside the plane, the ground and everything on it is moving, and they are not. This illustrates that being still and moving at constant speed are really akin to each other. From a particular vantage point, some things move and others do not. But, from another, those states of motion are reversed.
Now, what does Newton mean by the last part where he says that objects that seem to be resting are not really resting? Take anything on the Earth. Being on the surface of the planet, we perceive the Earth as a stable stationary home. But the Earth is in fact moving (it rotates round the Sun). From the Earth's perspective, the Sun is stationary. But the Sun is moving (it rotates around the center of the galaxy). To the Sun, the galaxy (as well as its center) are stationary. But they, in turn, fly across the universe. This is what Newton means when he implies that the state of motion is relative.
The license for this content is CC BY-SA 4.0