My Daughter, the Physicist

I recall a time when my young daughter could not form a sentence yet, but I recall thinking that she totally gets Newtonian Mechanics.  As a proud father, I was inclined to believe that she was a gifted 15-month-old, but I'd observed other toddlers, and must admit that they too demonstrate a solid understanding of Mechanics, the oldest branch of Physics.  To be clear, these thumb-sucking individuals would struggle mightily in my Mechanics course, let alone get through the three-hour final without wetting themselves.  

 Without basic linguistic or mathematical skills, a baby cannot be expected to understand or express the laws studied in the course or solve computational problems (their unrefined motor skills lead to calculation errors).  However, these diaper-clad kiddies perform experimental studies in classical physics on a daily basis.  Every day, as they learn to exist within their environment, they make observations on the laws that govern it.  Through experience, they discover how to thrive within these universal constraints.

Newtonian Mechanics is, in a way, the oldest branch of science.  It deals with the most basic manipulation of our environment.  In essence, Mechanics is the study of motion of matter, or mass. 

There are many correct, yet distinct ways to conceive of mass.  Chemists think of it as a quantity of matter.  I have two preferred definitions.  My favourite is "resistance to translational acceleration" followed closely by "ratio of weight force to gravitational field."  A theoretical physicist would likely offer a fourth definition that has been debated for many decades, before it received experimental confirmation in recent years: "blah blah blah Higgs Boson blah blah blah."

A primitive invention such as the wheel is a mechanical device man has used in a variety of ways for millennia.  Although the nature of how a wheel works has been clear since its inception, the physical laws governing the motion of a rolling wheel were derived by Isaac Newton in the seventeenth century.  The foundation of classical Physics, which Einstein later proved apply only to things moving much slower than the speed of light and very far from enormous masses, was laid by Newton’s Three Laws of Motion. 

The First Law says that a moving body will only change its velocity if an external force is applied to it.  This is evident enough – it means that a puck would slide down the ice indefinitely if not for the contact force known as friction between it and the ice surface as well as the drag force imparted by the in its way.  These two forces (electromagnetic in nature, like most forces) point opposite to the puck's direction of motion.  One correct though not general interpretation of this law is that an object at rest remains at rest if the net force acting on it is zero.

Newton’s Second Law is indeed the cornerstone of Mechanics.  An economics student must leave an introductory class with an understanding of “Supply and Demand” – I ask that if students retain just one thing from my Mechanics course, it be that F = ma.  The bold notation signifies a vector quantity (an entity that has a direction).  This simple equation means that the net force is equal to the mass multiplied by the acceleration.  

Otherwise stated, the magnitude and direction of the acceleration of a body is equal to the magnitude and direction of the net force acting on it divided by its mass (a = F/m).  The acceleration of a body means its rate of change of velocity (how quickly its speed and/or direction is changing), and net force means the sum of all external forces acting on it.  Note that the first law is simply a result of the second law for the case when the net force is equal to zero. 

The Third Law is perhaps the most confusing, but may be stated very simply: “For every force applied by body one onto two, there is an equal and opposite force applied by body two on one,” so all forces come in pairs.  We call such pairs third law pairs, and for every interaction in nature, there exist two forces.  These forces cancel if and only if we are looking at both bodies involved in the interaction as a group.  The two forces then become internal to the system, and can be neglected in our analysis.  When we examine any single body, each and every force becomes relevant as they are all external.  

When a fly hits the windshield of a car cruising down the highway, the windshield imparts the same contact force onto the fly as that imparted by the fly onto the windshield (the windshield is not bothered by this magnitude of force, while the fly will need two Advil at best).  It is noteworthy that the magnitude of force during this sad and final collision in the life of the fly actually changed during the very brief (milliseconds long) collision.  When a force is imparted for some time, we actually refer to the cumulative effect as a linear impulse.  It is thus true, also by Newton's Third Law, that the impulse by the windshield onto the fly is equal in magnitude, but opposite in direction to that by the fly onto the windshield.

Imposing these laws, particularly the second and third, allows one to solve a wide array of mechanical problems.  An understanding of Newton’s laws allows for a deeper appreciation of Mechanics, but is not necessary for a basic appreciation.  When my daughter was six months old, she already knew that letting things go caused them to drop to the ground.  She had discovered the law of gravitation, which says that all mass is attracted to other mass, particularly the nearest, largest mass.  On the surface of the Earth, the only gravitational force of consequence is the one established between all objects and Earth as a whole, which is a considerably large mass.   

My daughter's understanding of gravity deepened as she learned to walk.  Every time she fell down, and converted her gravitational potential energy into kinetic energy, and she hit the ground with a thump.  In the process, she learned about surface hardness, as the harder surfaces, like our wood floors, applied a larger applied force to her rear end than the softer carpeted areas (this happens because the collisions with the carpet last a touch longer, allowing the impulse to be spread out over a longer period of time).

The next physics lessons involve projectile motion.  It turns out that the only thing more fun than dropping stuff is throwing it.  The curved path followed by the objects she throws is due to the relatively unchanging horizontal component of the ball's velocity and its downward relatively uniform acceleration.  Greater initial velocities yield greater distances.  The study of motion in space and time (not why they occur) is a branch of mechanics known as kinematics, and she is becoming well-versed in it.

There are endless mechanical conclusions to be gathered whenever we go to the park.  An introductory physics class could bring a stop-watch to a park, and the setting would suffice for the majority of their experiments.  As she accelerates down the slide, she is learning about motion along an inclined plane with friction, a topic that many students struggle with.  

As we take a break from the see-saw and sit in equilibrium, she learns about the principle of torque, like that used in levers – as I sit eight times closer to the pivot point than she, my weight, which is eight times greater than hers, causes an equal and opposite torque to counteract hers.  Finally, she displays simple harmonic motion as she vibrates back and forth in the swing.  Now that she is older, she can swing all by herself.  How you ask?  She does so by adding well-timed (well-phased) angular impulses about the pivot point, thereby increasing her angular momentum about the pivot point; in so doing, the kinetic energy of the system increases and this allows her to reach new heights.

I look forward to teaching her about electricity and magnetism (she has fortunately not discovered that one on her own first via electrical outlets in our home).  Maybe I will teach her about Einstein’s theories of relativity.  

Some kids have normal parents, who buy their girls normal toys.  My daughter has an abnormal father who feels that our home lacks a mass and pulley system.  I would be lying if I said that bedtime stories at my house never include how the Universe has matured from the Big Bang to this point in history.  It is a blessed time.  It is a time when my eldest daughter can ask why the Earth spins how fast it spins and I can answer her.  It is a time when my youngest daughter asks how the smartest monkey became a human, and my wife can answer her. 

My daughters may become 'nerds', but the negative connotation that was once attached to that term has long dissolved.  I am proud that my children will be ready to face the universe by understanding the laws that appear to be governing it.   

In truth, no matter how much I try to teach my children about Physics, their real appreciation for it will come from pushing up against its boundaries themselves, by throwing stuff and playing in the park.  We tend to learn things best when we teach them to ourselves.  People tend to excel at things they are naturally drawn to.  I will try to let them decide for themselves if Physics is interesting. And then, if they decide wrong, I will be calm and collected when I explain to them why they are wrong.  Amen.

It is common for a Physics student to express their lack of understanding of Physics principles.  I sometimes wish that my students realized just how much they already understood about Physics before they entered my classroom.