Laws of Motion
For 2000 years, philosophers believed Aristotle: an object moves only if something pushes it, and it stops when the push ends.
Start with the simplest version: this lesson is about Laws of Motion. If you can explain the core idea to a friend using everyday language, examples, and one clear reason why it matters, you have moved from memorising to understanding.
For 2000 years, philosophers believed Aristotle: an object moves only if something pushes it, and it stops when the push ends. Then Newton revolutionized physics with three simple laws that changed our understanding forever. These laws connect force, mass, and acceleration, and they explain everything from why seatbelts save lives to why the moon orbits Earth. Understanding these laws is the key to mechanics.
Aristotle's Fallacy
Aristotle thought objects have a natural tendency to be at rest, and motion requires constant force. If you push a ball, it moves; when you stop pushing, it stops. This seems obvious from experience—but it's wrong.
What really happens? Friction and air resistance act on the ball in the opposite direction of motion. If you could eliminate these forces, the ball would continue forever. Aristotle confused the presence of friction with a fundamental law of motion. This "fallacy" shows how careful observation and experimentation trump intuition.
Newton's First Law: Inertia
"An object at rest remains at rest, and an object in motion remains in motion, unless acted upon by an external force."
This is the principle of inertia. Objects resist changes in their motion. A soccer ball on a frictionless surface will roll forever in a straight line without any force pushing it. Your body's inertia is why you lurch forward when a car brakes—your body "wants" to continue forward at constant velocity.
The first law defines force: it's what causes acceleration. No force means no acceleration, which means constant velocity (or rest, which is velocity = 0). A force is a push or pull that changes motion.
Inertia is related to mass. A heavier object (more mass) has more inertia—it requires more force to produce the same acceleration. Inertia and mass are proportional.
Newton's Second Law: F = ma
"The acceleration of an object is proportional to the net force applied and inversely proportional to its mass."
This is physics' most famous equation: F = ma
Force equals mass times acceleration. A small force produces small acceleration; a large force produces large acceleration. A large mass resists acceleration (requires more force for the same acceleration); a small mass accelerates easily.
Think of it this way: pushing a skateboard requires little effort (small mass), but pushing a car requires enormous effort (large mass) to produce the same acceleration. The net force is the vector sum of all forces. If multiple forces act on an object, their total (net) effect determines acceleration.
Units: Force is measured in newtons (N). One newton accelerates 1 kg by 1 m/s², so 1 N = 1 kg·m/s².
Newton's Third Law: Action-Reaction
"For every action, there is an equal and opposite reaction."
When you push on a wall, the wall pushes back on you with equal force. When a rocket burns fuel and ejects gas downward, the gas exerts an equal upward force on the rocket. These forces are equal in magnitude but opposite in direction, and they act on different objects.
Critical insight: action-reaction pairs never cancel each other because they act on different objects. When you jump, your legs push down on Earth (action), and Earth pushes up on you (reaction). The upward force on you accelerates you upward. Earth also accelerates, but its enormous mass makes the acceleration imperceptible.
This law explains seemingly impossible feats. A rocket in space (with no air to push against) moves by ejecting mass backward. The expelled mass experiences a backward force; the rocket experiences an equal forward force. Newton's third law makes this possible.
Types of Forces
Gravitational force: The earth pulls you downward with force F = mg, where g ≈ 10 m/s² is gravitational acceleration.
Normal force: When you stand on ground, the ground pushes upward on you. This normal force balances gravity (at rest) or combines with gravity to produce net acceleration (accelerating elevator).
Friction: Opposes motion. Static friction prevents an object from starting to move; kinetic friction opposes motion once it's underway. Friction = μN, where μ is the coefficient of friction and N is normal force.
Tension: The pulling force in a string or rope. A rope can only pull, never push.
Applied force: Any force directly applied to an object.
Free-Body Diagrams
A free-body diagram shows all forces acting on a single object as arrows. Drawing these clarifies problems. For a box being pushed on a table:
- Applied force (forward)
- Friction (backward)
- Weight (downward)
- Normal force (upward)
The net force (vector sum) determines acceleration via F = ma. If net force is zero, the object moves at constant velocity or remains at rest.
Conservation of Momentum
Consider two balls colliding. Each experiences a force from the other. By Newton's third law, these forces are equal and opposite. If the collision lasts the same time for both, the change in momentum (impulse = force × time) is equal and opposite.
Momentum = mass × velocity. In an isolated system (no external forces), total momentum is conserved. This explains collisions, explosions, and rocket propulsion.
If a cannon fires a cannonball, momentum is conserved: the cannon and cannonball separate with momenta equal and opposite. The cannon recoils backward; the ball shoots forward.
Applications: Why Seatbelts Work
Without a seatbelt, you continue moving forward at the car's velocity (Newton's first law). When the car hits an obstacle and stops suddenly, the dashboard or windshield provides the force to stop you. If the force is too large, injury occurs. A seatbelt applies this stopping force more gently over the chest and abdomen (spread over time and area), reducing injury. It harnesses Newton's second law: same change in momentum, but distributed over longer time and larger area means smaller force.
Socratic Questions
- Aristotle thought constant force is needed for constant motion. Why does this seem intuitively obvious from everyday experience? What fact about the world makes Aristotle's fallacy so tempting?
- A book rests on a table. List all the forces acting on it. Which pairs are action-reaction pairs (Newton's third law), and which simply balance each other out?
- If F = ma, why do objects fall at the same rate regardless of mass? Wouldn't heavier objects experience more gravitational force?
- A rocket accelerates in space where there's no air. How does the rocket "push off" if there's nothing to push against? How do Newton's laws explain this?
- In a collision between a moving car and a stationary bicycle, both experience equal and opposite forces (Newton's third law). Why is the car's acceleration so much smaller than the bicycle's?