Class content > Newton's Laws > Newton's Laws as Foothold Principles
Prerequisites
Newton's second law is written quite simply:
But a large set of quantitative conceptual ideas are packed into interpreted and making sense of what this equation is telling us. Each symbol in the equation reminds us of some important conceptual idea. Let's make sense of N2  "see the dog in the equation"  by unpacking what you have to know in order to understand this simpleappearing relationship.


1. a  The thing on the left of the equation is the acceleration. To understand that, we have to understand the whole array of specifying an object's position (Coordinates) and how that position changes (derivatives, velocity, acceleration). This means (for motion in one dimension) we need the definitions
It's important to note that the acceleration is written on the left. We do this to remind ourselves that it's the forces that cause the acceleration rather than the other way around. Though of course if we know the acceleration and mass we can find the net force.
2. A  Each of the variables has a subscript labelled which object we are talking about. This reminds us that a fundamental assumption of the Newtonian framework is that we best understand what is happening by considering individual objects and figuring out what influences are acting on them (Object egotism). Each object we consider will have its own Newton 2 equation. The subscript A on F^{net}
reminds us that it is the forces that the object feels that controls its motion. (The forces it exerts have effects on the motion of the objects it exerts them on.)
3. F  To interpret this we need to understand that it is the interactions with other objects that cause the object we are considering to change its motion (accelerate). And we need to understand how this force is quantified by an operational definition.
4. net  This little superscript holds a lot of conceptual ideas. First, that it is the (vector) sum of the forces that an object feels that results in its acceleration. Each individual force does not produce an individual acceleration. When we break out this sum explicitly,
the subscripts on the individual forces remind us that every force is caused by another object. Further, that the forces we want to include are all the forces exerted by other objects on the object we are considering.
5. m  Dividing the net force by m (subscript A) reminds us that the resulting force on the object is shared over the parts of the object. A bigger object will have less of a response (acceleration) to the same force.
6. → The little arrows on top of the acceleration and net force remind us that Newton's second law is a vector equation. This means that each perpendicular direction has its own Newton's law  x, y, and z. Further, that it is the net force in the x direction that affects the motion in the x direction, the net force in the y direction that affects the motion in the y direction, etc.
That's a lot to pack into one little equation with what looks like 3 symbols (that turn out to be 6). But each of these ideas is an essential piece of making sense of this important principle.
Joe Redish 9/20/11
Comments (0)
You don't have permission to comment on this page.