3.2 Newton’s great synthesis

Learning objectives

By the end of this section, you will be able to:

• Describe Newton’s three laws of motion
• Explain how Newton’s three laws of motion relate to momentum
• Define mass, volume, and density and how they differ
• Define angular momentum

It was the genius of Isaac Newton that found a conceptual framework that completely explained the observations and rules assembled by Galileo, Brahe, Kepler, and others. Newton was born in Lincolnshire, England, in the year after Galileo’s death ( [link] ). Against the advice of his mother, who wanted him to stay home and help with the family farm, he entered Trinity College at Cambridge in 1661 and eight years later was appointed professor of mathematics. Among Newton’s contemporaries in England were architect Christopher Wren, authors Aphra Behn and Daniel Defoe, and composer G. F. Handel.

Isaac newton (1643–1727), 1689 portrait by sir godfrey kneller.

Newton’s laws of motion

As a young man in college, Newton became interested in natural philosophy, as science was then called. He worked out some of his first ideas on machines and optics during the plague years of 1665 and 1666, when students were sent home from college. Newton, a moody and often difficult man, continued to work on his ideas in private, even inventing new mathematical tools to help him deal with the complexities involved. Eventually, his friend Edmund Halley (profiled in Comets and Asteroids: Debris of the Solar System ) prevailed on him to collect and publish the results of his remarkable investigations on motion and gravity. The result was a volume that set out the underlying system of the physical world, Philosophiae Naturalis Principia Mathematica . The Principia , as the book is generally known, was published at Halley’s expense in 1687.

At the very beginning of the Principia , Newton proposes three laws that would govern the motions of all objects:

• Newton’s first law    : Every object will continue to be in a state of rest or move at a constant speed in a straight line unless it is compelled to change by an outside force.
• Newton’s second law    : The change of motion of a body is proportional to and in the direction of the force acting on it.
• Newton’s third law    : For every action there is an equal and opposite reaction ( or: the mutual actions of two bodies upon each other are always equal and act in opposite directions).

In the original Latin, the three laws contain only 59 words, but those few words set the stage for modern science. Let us examine them more carefully.

Interpretation of newton’s laws

Newton’s first law is a restatement of one of Galileo’s discoveries, called the conservation of momentum . The law states that in the absence of any outside influence, there is a measure of a body’s motion, called its momentum    , that remains unchanged. You may have heard the term momentum used in everyday expressions, such as “This bill in Congress has a lot of momentum; it’s going to be hard to stop.”