## Physics: Newton’s Laws of motion

Newton’s laws of motion are three physical laws that laid the foundation for what we now call classical mechanics. These laws describe the relationship between a body, forces acting upon it, and its motion in response to those forces. Newton used these laws to explain and investigate the motion of the world around him.

Newton was a true giant of science. Necessity might have even led him to invent modern calculus as a mere detour in his work. Learning about this man is well worth our time.

### History

The ancient Greek philosopher Aristotle originally proposed that everything in the universe has a natural place. Rocks wanted to rest on earth and smoke wanted to rest in the sky. Everything wanted to be at rest and in order for them to move, an outside agent would need to continually propel it.

Kepler, building on the observations of Tycho Brathe, postulated that the orbits of planets were ellipses. This insight was important because it allowed Kepler to form a clean casual explanation for the motion of planets.

Galileo, at roughly the same time as Kepler, was forming abstract mathematical laws for the motion of everyday objects. The famous cannon experiment showed that a heavier object and a lighter object fall and hit the ground at the same time. The insight that Galileo drew from this, is that a force is necessary to change the velocity of an object, but no force is needed to maintain that velocity. In the absence of a force, both falling cannon balls would continue moving at the same velocity despite their different sizes. Galileo referred to this tendency of objects to resist change as inertia.

In 1687, Newton published the Mathematical Principles of Natural Philosophy, which built on these previous insights. Newton’s work differed from earlier works by using proper scientific and mathematical methods. The previous ideas were either incomplete, or incorrect, but Newton changed all of this. His work is the foundation of modern classical mechanics and helps us to understand the world around us.

### Newton’s first law – the law of inertia

Law 1: An object in motion will remain in motion, and an object at rest will remain at rest, unless acted upon by a force.

This law basically states the tendency of an object to keep doing what it is doing. As Galileo originally postulated, in order to accelerate something, you need to have a net force acting on it. Newton expanded on this idea and formulating a way of measuring inertia. Why is it harder to accelerate a boulder than it is to accelerate a feather? Why does one object seem to have more inertia? Newton explained that inertia is a function of mass. The more mass an object as, the harder it is to move.

### Newton’s second law – the law of acceleration

Law 2: Net force is equal to mass times acceleration

More usefully put, acceleration is equal to force divided by mass. This insight builds upon the insight on inertia. The more massive an object, the harder it is to move. The more force applied to an object, the easier it is to move. It is worth highlighting that we are talking about net forces here, meaning the summation of all forces. When all forces on an object cancel each other out, the object would be said to be in equilibrium.

Gravity is the most common force in our daily lives. Acceleration due to gravity is 9.81m/s^2. When we use this to solve for the force of gravity we get an answer that is measured in kg(m)/s^2 . We refer to this unit as newtons. All forces are measured in newtons.

Gravity isn’t the only force acting on an object, and when considering net force we need take them all into account.

### Newton’s third law – the law of symmetry

Law 3: For every action, there’s an equal but opposite reaction.

If you exert a force on an object, it exerts a reaction force back on you. The normal force is one example of this reaction force. The normal force is always perpendicular to whatever surface an object is on. For example, if you lay a rock on a table, the force of gravity would be accelerating the rock downward, and the normal force would be accelerating the rock upward. The two forces cancel each other out and the net force is zero. If the normal force can’t match the force of gravity, the table would break. A tension force works in the same way, but it is a pulling force rather than pushing force. For example a rock hanging from a rope.

A question now arises, if action and reaction forces are constantly equal, how can anything move? Basically, things move because there are more things going on than just the action and reaction forces. For example, if we pull on a cart, the cart pulls back on us. But we are still able to move it. This is because we are also pushing backward on the ground and at the same time the ground is pushing forward on us. If the force of the ground pushing us forward is greater than the force of the cart pulling us back, we will move.

Lets combine all of this into an example.

Imagine we are in an elevator that is attached to a counterweight on a pulley system. We can calculate how fast we will accelerate down based on all of the forces acting on the system.

elevator net force = tension force – massElevator * g = massElevator * accel

counterweight net force = tension force – massCounter * g = massCounter * accel

Using algebra we can combine and rearrange these two equations to solve for acceleration.

a = g(massE – massC) / (massE + massC)

or

acceleration = net force / mass

where our net force is acceleration due to gravity multiplied by the difference in masses and our mass is the total mass in the system. Everything comes full circle.

### Limitations of Newton’s laws

Newton’s laws are an excellent approximation for motion at the scales and speeds of everyday life, but they break down at very small scales, very high speeds, and around very strong gravitational fields.

In the case of macroscopic objects approaching the speed of light, relativistic mechanics is needed. In the case of microscopic objects at normal speeds, quantum mechanics is needed. And in the case of microscopic objects approaching the speed of light, quantum field theory is needed.

Newtonian mechanics is a simplification or approximation of more accurate theories like general relativity. However, it still serves us well with day-to-day objects.

### Modern physics

In modern physics, Newton’s laws have been replaced by the laws of conservation of momentum, energy, and angular momentum. These laws apply to both light and matter, and are therefore thought to be more valid.

Law of conservation: Momentum, energy and angular momentum cannot be created nor destroyed.

Force is simply a time derivative of momentum, so the concept is subordinate and no longer used in fundamental theories.

### In relation to investing

Every action has an equal but opposite reaction, much like every buy order in the stock market has an equal and opposite sell order. The side with more momentum will win in the end. When making a purchase, one should weigh how much weight the opposite thesis has. Like Charlie Munger says, always invert.

The most important concept in economics is the law of unintended consequences. Much like Newton’s third law, actions that a state take will have consequences that may be opposite in nature. The classic example of this, is giving people money to kill snakes in order to eliminate a snake problem. This has been shown to incentive people to breed more snakes in order to get more money. The original action meant to reduce the snake population, actually ends up increasing it. We should always be aware of unintended consequences to our actions.

### Conclusion

More than anything else, the study of physics gives us an insight into how reality actually works. If I roll a bowling ball at some pins, physics allows me to calculate why exactly it always ends up in the gutter. This basic mental model of cause and effect helps us understand the world around us and allows us to make better judgements in seemingly unrelated matters.

References: