Force and Momentum: Exploring a Point of Intersection Between Classical and Modern Physics

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From the Initiative for the Renewal of Science Education series.

At the beginning of every year in physics, I start out with an overview of Aristotle’s ten categories of being:

This diagram shows that the most fundamental category is “substance”:

  • It “stands under” the other nine accidents, supporting them.
  • It cannot be directly sensed by any of the five senses.
    • Impossible to directly see, hear, touch, smell or taste a substance (we only see, hear, touch, smell or taste the accidents)
  • The substance is only grasped by the intellect as the intellect abstracts from the information we receive from our senses.

The categories of “quantity” and “quality” are intrinsic to the substance itself, what our senses can grasp about the substance.

The upper seven categories are extrinsic to the substance, having to do with the being of a thing in its particular surroundings and circumstances.

Most of the students find this to be a fun and interesting start to the year. We get to look at all kinds of fun questions such as “Can you have half a horse?” or “Is something intrinsically ‘big’ or only ‘big’ in relation to other things?” and the classic “Is water wet?” This is not meant to be a pedantic and thorough analysis of every edge case, but rather it gets the students thinking about the real world. What do these words mean: half, big, wet? And what does it mean for an object to “be” them?

We focus especially on the distinction between the intrinsic accidents of quality and quantity as opposed to the extrinsic accidents of action and passion. For action and passion, the basic idea is that for every two objects A and B, if A acts on B, it is also true that B is being acted up on by A. This is rather obvious, but also is the necessary prerequisite for understanding Newton’s Third Law of Motion: for every action there is an equal and opposite reaction. The most fundamental question in physics is “How do objects interact with each other?” Can an inanimate object “act” on itself? 

This leads to what many consider to be, both historically and practically, the most important concept in physics: momentum. How is it that when I throw a ball, it continues to move after it leaves my hand? The most common responses from students are “your hand,” “gravity,” and “the air.” Although all of these can be said to cause the ball to accelerate, these answers all fail to answer the fundamental question: why does it continue to move? In other words, if there was no gravity from Earth, no air, and my hand ceased to exist after it let go of the ball, would the ball still move? Almost all the students say that it would, so then the question is why? It turns out that this is one of the most difficult concepts for people both historically and presently to understand. I tell my students every year that it took human beings thousands of years to figure this out, so it’s worth spending at least a few days of class on it to really understand it. Of course, most students will continue to struggle with this throughout the year, but addressing it up front is an excellent way to set the stage for subsequent conversations.

The answer, of course, is that it moves because it has momentum, i.e., a quality of motion not due to passion, i.e., a reception of a force. Since everyone already understands color as a quality, I usually make an analogy with painting a desk. If I came into the classroom and painted the desk red, would I come into the room the next day and ask, “Why is the desk still red?!” Probably not, because I would understand that color is intrinsic, i.e., it inheres in the subject. If I were to ask “Why is the table still red?”, the students would be a bit baffled but respond with something simple like, “Well, it’s a red table, so it’s red” or “Nothing else caused it to not to be red, so it persists as red.” It is essential that a student come to realize that momentum works the same way. In physics, when we see that an object has a certain velocity, we should expect that that velocity stays the same, just like we expect its color to stay the same. Why? Because momentum, like color, is a quality. And quality is an intrinsic category. It’s also worthwhile to spend time discussing why it’s so counter-intuitive to think of momentum as a quality. Why is this concept so difficult? Well, because never in our experience does this actually happen. In our  experience, objects with a certain velocity are regularly turning, slowing down, or speeding up. If I hold an object stationary in the air and let go, it begins to move. If I kick a ball along the ground, it immediately starts to slow down. If I throw a ball to someone across the room it moves in an arc. The only time things continue at constant velocity in our experience is when we are applying a force to them, for instance in a car traveling at a constant speed down the highway. The students know that this requires a force to sustain the motion. This seems completely backwards from what we just talked about in the previous discussion on momentum. What gives? Well, this is where action and passion come in. All these things happen because they are being acted upon by external agents. Passion is an extrinsic category. The ball held up in the air, absent an external agent, would stay put. A ball kicked along the ground, absent an external agent, would continue to move at just that speed in just that direction. A ball thrown upwards to a friend would, absent an external agent, continue to move up and over our friend in a straight line at the same speed we threw it. This is quite a topsy-turvy world!

The study and learning of physics demands a vivid imagination. We must imagine what would happen without the earth around and without the air. This is hard enough for us, but how much harder it would have been before anyone had traveled outside of our atmosphere – or before the telescope! Our imaginations are aided by movies and film that recreate this experience for us, and so it is much easier for us to imagine motion absent an external agent. It’s good to instill in the students an appreciation for how difficult it was throughout history to come to these conclusions and how these conditions of nature were eventually understood.

To bring it all together, the key lesson I want students to understand is that momentum is a quality whereas force is an interplay of action and passion. In other words, objects will, absent a net force, continue at constant velocity; and the contrapositive, that if an object is not maintaining a constant velocity, there must be an external agent acting upon it, i.e., it is experiencing passion. When an external agent acts upon an object in a manner which by nature would alter the object’s velocity, then we say that this agent is applying a force to the object. Thus force is an action/passion relationship, and momentum is a quality.  

Dave Maxham

About the author:

Dave Maxham

David Maxham grew up in New Jersey and went to Rutgers College, majoring in Mathematics and minoring in Classics, also studying linguistics and psychology. Before coming to The Heights in 2013, he taught high school math in the public schools for four years, in Newark, New Jersey and Dunellen, New Jersey. He loves music and plays the piano and guitar. He lives in Maryland with his wife, Samantha, and seven children.