Abers and Kennel write in Matter in Motion, “Newton’s first two laws had been proposed in various forms by Galileo, Hooke, and Huygens.
Newton’s third law is completely original, and makes the laws of mechanics logically complete.” According to Newton’s Third Law of Motion, for every action, there is always an equal and opposite reaction. In other words, all forces occur in pairs of forces that are equal in magnitude and opposite in direction.
This law is perhaps most apparent when considering objects that touch:
The downward force of a spoon on the floor is equal to the upward force of the floor on the spoon. The law also holds for objects that gravitationally 96 | a r c h i m e d e s t o h a w k i n g
attract one another. For example, a bird in flight actually pulls up on Earth with the same force that Earth pulls down on the bird. If a person falls to the ground, the person’s force on Earth is the same as Earth’s force on the person. However, due to the much larger mass of Earth, Newton’s Second Law predicts that the acceleration of Earth will be much smaller than the person’s acceleration. In outer space, not only does a comet accelerate toward the Sun, but the Sun accelerates toward the comet.
Notice how these examples of Newton’s Third Law employ forces of the same kind. As another example, if a grassy lawn exerts a frictional force on the accelerating tires of the toy wagon, Newton’s Third Law predicts that a frictional force exists corresponding to the tires pushing backward on the lawn. Newton himself gave an example in his own words: “If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied by a rope, the horse will be equally drawn back towards the stone.”
The law is sometimes mathematically written as FBA= −FBA.
If body A exerts a forceFBAon body B, an equal but opposite forceFBA
is exerted by body B on A.
One consequence of the Third Law is that the sum of the momenta of two objects that exert force upon each other remains constant through time. This statement assumes that no other forces are interacting with the objects, and it applies reasonably well, for example, to the study of two billiard balls just before and after collision. In fact, Newton studied the momentap1and p2of bodies 1 and 2 before and after collisions, and he understood that the momentum was conserved such that the sum ofp1+ p2was constant.
Newton’s Third Law even implies that when a basketball player throws a basketball at the floor, Earth should move! However, the basketball player does not observe Earth move for several reasons. For simplicity, assume that the basketball weighs 1 kilogram and moves at 100 kilometers an hour when it hits the basketball court floor that is coated with glue so that the basketball sticks upon impact. The momentum of the ball just before it hits the floor isp=mv= 100 kg·km/s. After the collision, Earth acquires this momentum. Let’s calculate the change in Earth’s speed. Let ME be the mass of Earth, and vE its change in speed. Then we have 100 =MEvEorvE= 100/ME. Given that the mass of Earth is very roughly ME= 5.9742×1024kilograms, the change in the speed of Earth is roughly vE = 1/(5.9742 × 1022) km/h—a very small change indeed! In fact, this speed is less than two billionths of a billionth of a centimeter per hour or a speed equivalent to about a proton-width movement a year. Because the
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mass of Earth is so large, the tiny change in speed is immeasurable. In real- ity, Earth is not moved at all by the basketball. The interaction between the ball and Earth is dominated by countless other effects, including the conversion of some of the energy of interaction to heating the floor at the point of contact—and the prancing of animals, the crashing of raindrops, and movement of ocean waves.
Today, if you ask your friends if the planets in our Solar System revolve around the Sun, most will say yes. However, because of Newton’s Third law (for every action there is an equal and opposite reaction), we know that a planet does not does not orbit around a stationary Sun as Johannes Kepler believed. Instead, Newton suggested that both the planet and the Sun orbit around the common center of mass located between the planet and the Sun, and this requires scientists to modify Kepler’s Third Law to make it somewhat more accurate. However, Newton’s correction is small because the Sun is much more massive than any of the planets.
For a large planet such as Jupiter, the common center point is actually located outside of the surface of the Sun. Of course, when viewed from an even more complete perspective, the situation becomes more complex.
Like all stars, the Sun itself moves through space. It’s fast—20 km/s (45,000 miles/hour) with respect to nearby stars. Think of the Sun as a Ferrari that drags along nine planets in its interstellar race. When considering the entire galaxy, the Sun also moves in a nearly circular orbit around the galactic center—with a speed of 220 km/s.
Many physicists whom I consulted said that Newton’s Third Law was the most novel and original of Newton’s three Laws of Motion. Arons writes inDevelopment of Concepts of Physics,
All the other concepts we have encountered had a prior history of development and discussion, but historians can find no precedent for Law III in the writings of other investigators, nor is there any explicit indication of it in any of Newton’s own writings prior to the Principiain 1687.
These three laws are the foundations of classical dynamics and were mostly unquestioned until the early 1900s. Today, we know that when objects have velocities approaching the speed of light, Newtonian dynam- ics can fail and must be considered within the framework of Einstein’s Special Theory of Relativity. In particular, for high-speed objects, momen- tum is not simply the classical p=mv but a slightly more complicated expression, namely,p=mv/(1−v2/c2)1/2, wherecis the speed of light in a vacuum. Similarly, the postulates of quantum theory become important when considering the realm of the ultrasmall, such as size scales involving atoms and subatomic particles.
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Technically speaking, the laws of motion are valid only ininertial refer- ence frames, which are moving at constant velocity. Although the surface of Earth is not an inertial reference frame—because Earth is rotating on its axis and revolving around the Sun—for many real-world experiments, the surface of Earth can be treated as inertial.
Newton’s genius was that he provided a complete system and frame- work for our understanding of how the universe works for everyday objects traveling at speeds we encounter in our daily lives. We still use these laws for practical problems involving bullets, baseballs, and rockets.
While it is true that researchers such as Galileo made significant discov- eries in classical mechanics, it was Newton who formulated a complete system.