Foundations of Physics for Polymaths
Classical Mechanics
The Rules of Motion
The universe isn't chaotic. It follows predictable rules, especially when it comes to how things move. For centuries, people tried to puzzle out these rules. It was Isaac Newton who finally laid them out clearly. His three laws of motion are the bedrock of what we call classical mechanics, explaining everything from a thrown ball to the orbit of the moon.
An Object's Stubbornness
Newton's first law is all about inertia. In simple terms, objects are stubborn. They want to keep doing whatever they're already doing.
If an object is sitting still, it will stay still. If it's moving, it will keep moving at the same speed and in the same direction. It will only change its state of motion if an outside force pushes or pulls on it.
Think about a hockey puck gliding across a perfectly smooth sheet of ice. It will keep sliding in a straight line forever, or at least until it hits a wall or friction from the ice slows it down. The puck's tendency to keep moving is its inertia.
Inertia is an object's resistance to any change in its state of motion.
You feel inertia all the time. When a bus you're on suddenly stops, your body lurches forward. Why? Because your body wants to keep moving at the speed the bus was going. The bus stopped, but your inertia carried you forward until the seat or a handrail applied a force to stop you.
The Math of a Push
Newton's second law gives us a precise way to calculate how an object's motion changes. It connects three key ideas: force, mass, and acceleration.
- Force () is any push or pull.
- Mass () is a measure of how much stuff an object contains. More mass means more inertia.
- Acceleration () is any change in velocity—speeding up, slowing down, or turning.
This law states that the force applied to an object is equal to its mass multiplied by its acceleration. It's one of the most famous equations in all of physics.
Imagine pushing a small shopping cart and then a heavily loaded one. To get the loaded cart moving at the same acceleration as the empty one, you need to apply a much greater force. This is in action. A larger mass requires a larger force for the same acceleration.
Every Action Has a Reaction
Newton's third law is probably the most quoted, but it's often misunderstood. It says that for every action, there is an equal and opposite reaction.
This means forces always come in pairs. When you push on a wall, the wall pushes back on you with the exact same amount of force. When a rocket expels gas downwards (the action), the gas pushes the rocket upwards (the reaction), launching it into space. You can't have one without the other.
If object A exerts a force on object B, then object B simultaneously exerts a force on object A that is equal in magnitude and opposite in direction.
This might seem strange. If the forces are equal and opposite, why does anything move? When you push the wall, you feel the force, and the wall feels the force. But you and the wall are separate objects with different masses. The force is enough to move you (if you're on skates, for example), but it's not enough to move the massive wall. The forces are equal, but their effects on different objects can be very different.
Universal Currencies
Beyond Newton's laws of motion, classical mechanics is built on two powerful principles of conservation: the conservation of energy and the conservation of momentum. These are like accounting rules for the universe.
The laws of mass, linear momentum, angular momentum, and energy, together with Newton’s laws of motion, gravitation, and electromagnetism, constitute the physical framework from which much of classical engineering analysis is constructed.
First, the Law of Conservation of Energy. This law states that energy cannot be created or destroyed; it can only change from one form to another. The total amount of energy in an isolated system always remains constant.
A roller coaster at the top of a hill has a lot of potential energy (stored energy due to its height). As it races down, that potential energy is converted into kinetic energy (the energy of motion). The total energy—potential plus kinetic—remains the same throughout the ride (ignoring friction).
Second is the Law of Conservation of Momentum. Momentum is a measure of an object's motion, calculated as its mass times its velocity (). Like energy, the total momentum of a closed system (one with no external forces acting on it) never changes.
This is the principle behind a Newton's cradle. When you lift and release one ball, it strikes the others, and one ball on the opposite end swings out. The momentum of the first ball is transferred through the stationary balls to the last one, which then moves.
These five principles—Newton's three laws and the two conservation laws—form the essential toolkit for understanding the motion of everyday objects. They allow us to predict the paths of baseballs, design safe cars, and send probes to other planets.
Time to test your knowledge of these fundamental laws.
You're a passenger in a car that suddenly stops. You feel yourself lurch forward. Which of Newton's laws best explains this phenomenon?
According to Newton's Second Law (), if you apply the same amount of force to two objects, one with a small mass and one with a large mass, which object will have the greater acceleration?
With these concepts in hand, you have a solid foundation for exploring the mechanics of the world around you.


