The Laws of Dynamics — From Galileo to Newton

Few moments in the history of science are as transformative as the discovery of the laws of motion. In Chapter 9–1 of The Feynman Lectures on Physics, Richard Feynman captures this transformation with his characteristic clarity and enthusiasm. He opens the chapter with an almost dramatic statement: before Newton, the movements of the heavens were a mystery; after Newton, the cosmos itself seemed to obey a comprehensible mathematical order. Pendulums, planets, and springs could all be described by the same underlying principles.

Feynman’s goal in this chapter is to guide the reader through that same intellectual journey - from mystery to understanding - showing how Newton’s laws of motion turned vague intuition into precise physical law.

Galileo and the Birth of Inertia

Feynman begins with Galileo, whose insight into motion marked the first great leap forward. Galileo recognised that an object not acted upon by an external influence would continue to move at a constant speed in a straight line - or remain at rest if it were already still. This was the principle of inertia, a radical departure from the Aristotelian belief that continuous motion required a continuous cause.

Feynman uses an everyday example: a block sliding across a table. In real life, it quickly comes to rest - but, Feynman reminds us, that’s only because it rubs against the table. If the friction could be removed, the block would keep gliding indefinitely. Galileo’s brilliance lay in imagining away the complicationsof the real world to reveal the pure principle underneath.

This act of imagination - separating the ideal law from the messy world - becomes a recurring theme in Feynman’s teaching. It’s not that nature always behaves ideally, but that understanding begins when we strip the problem to its essence.

Newton’s Leap: From Inertia to Dynamics

After Galileo’s insight came Newton’s great synthesis. Feynman points out that Galileo gave us the rule for what happens when nothing acts on an object; Newton told us what happens when something does. This “something” is the force, and it produces a change in the object’s motion - specifically, a change in its momentum.

Feynman then introduces Newton’s Second Law of Motion in its most general form.

At first glance, it looks simple, but Feynman pauses to unpack its subtleties. Momentum - the product of mass and velocity - is not just a fancy term for “motion.” It combines how fast something moves with how much matter is moving. A light ball and a heavy stone can have very different momenta even if they roll at the same speed.

This distinction allows Feynman to highlight a subtle but important concept: mass as a measure of inertia. The more massive an object, the more it resists a change in motion. We experience this intuitively when pushing a light ball versus a heavy one. Yet, as Feynman carefully notes, mass and weight are not the same thing. Weight depends on gravity -  it would change on Mars - but inertia does not.

Defining Force and the Constancy of Mass

Before proceeding, Feynman acknowledges that Newton’s equation hides many assumptions. For instance, it presumes that mass is constant - a simplification that works for most classical mechanics problems but eventually breaks down in relativistic physics. It also assumes that when we combine two bodies, their total mass is simply the sum of their individual masses. These may seem obvious now, but they were revolutionary ideas in Newton’s time.

Feynman also stresses that force is not merely a “push” or “pull” as we casually think of it. It’s something more precise - the mathematical quantity that causes a change in momentum. Moreover, the change in velocity it produces can involve not only speed but also direction. This is crucial for understanding motion in curves or orbits.

From Equation to Acceleration

If we take Newton’s Second Law and assume mass is constant, it simplifies elegantly:

F=ma

Here, acceleration is the rate of change of velocity - and as Feynman points out, velocity itself is a vector quantity, possessing both magnitude and direction. Thus, a force can change either or both. When a force acts in the same direction as motion, the object speeds up; when it acts opposite, the object slows down; and when it acts perpendicular to the motion, the direction changes - the object follows a curved path.

Circular Motion and Forces at Right Angles

To illustrate this, Feynman draws upon earlier discussions of circular motion (from Chapter 7). An object moving in a circle of radius R with speed v constantly changes direction, even though its speed may remain constant. The acceleration responsible for this curvature points toward the centre of the circle.

Whether it’s a planet orbiting the Sun or a stone swung on a string, the same principle applies - a force acting perpendicular to the motion keeps the object curving around, never flying off in a straight line.

From Springs to Planets

Feynman concludes the section by connecting these abstract principles to real examples - from oscillating springs to planetary perturbations. Before Newton, such problems were unsolvable mysteries. After Newton, they became calculable. The same law that governs a small mass on a spring also governs the slow, subtle deviations in the orbit of Uranus due to the gravitational tugs of Jupiter and Saturn. The scope of Newton’s law, Feynman emphasises, is astonishingly wide.

Why This Chapter Matters

Feynman’s treatment of Newton’s laws in Chapter 9–1 is not just a lesson in physics; it’s a lesson in thinking. He shows how progress in science often comes from daring to imagine an ideal world, defining quantities carefully, and accepting approximations where necessary. By the end of the chapter, the reader is not merely memorising equations - they are seeing motion itself in a new light.

From Galileo’s insight to Newton’s unifying law, and through Feynman’s lucid storytelling, the journey of dynamics becomes both historical and conceptual - a story of how we learned to describe, with precision and beauty, how things move.