## Laws of Motion A Historical Perspective

All living as well as nonliving objects that are large enough to be visible through a light microscope obey the laws of motion first formulated in mathematical terms by Sir Isaac Newton in 1687 in his book Philosophica Naturalis Principia Mathematica.

The first of the three laws Newton formulated is about the resting state: an object (body) remains at rest unless it is compelled to move by a force exerted on it. The first law stems from Galileo's assertion that "a moving body thrown on a horizontal plane, without any obstacle, will remain in uniform motion indefinitely if the plane extends to infinity." The first law is easy to grasp when we consider the behavior of an uncooperative, sulking dog. No amount of enticement, throwing a frisbee or offering a bone cookie, will make the dog move an inch; she pretends to be dead. An option is to pull on her leash and drag her. To do that, one has to overcome the frictional force exerted on the dog by the ground. Once the dog realizes she will not be able to resist the force of the leash as a paralyzed object, she might well reposition herself on the floor and try to balance the force of the leash with the contact forces acting on her paws.

As this example shows, a number of forces may act on an object that is at rest. According to the first law, a building is at rest because its weight is balanced vertically by the upward force exerted on it by the ground. A building will not move unless it is acted upon by wind or earthquake forces that cannot be balanced (Fig. 2.1a). A ballerina can stand still on the tiptoes of one foot by balancing the weight of her body with the contact force exerted by the ground. She is at rest, unless of course she loses her balance and the contact force exerted by the ground is no longer equal and opposite to the force of gravity (Fig. 2.1b). In the diagrams of Fig. 2.1 we have identified all the forces that act on a given body. Such diagrams are called free-body diagrams.

Newton's second law is the fundamental law of motion. According to the second law, an object will accelerate in the direction of the unbalanced Figure 2.1a,b. Objects in static equilibrium: the Pisa tower (a), and a ballerina (b) holding a delicate balance on the toes of her one foot. The arrows in the figure indicate the forces acting on each object. The symbol W usually denotes the weight of a body and N is the ground force exerted on the body.

Figure 2.1a,b. Objects in static equilibrium: the Pisa tower (a), and a ballerina (b) holding a delicate balance on the toes of her one foot. The arrows in the figure indicate the forces acting on each object. The symbol W usually denotes the weight of a body and N is the ground force exerted on the body.

force. The magnitude of acceleration will be equal to the magnitude of the resultant (unbalanced) force divided by the mass of the object. If an object is at rest or moving with constant velocity, the resultant force acting on the object must be equal to zero.

The path toward the precise formulation of the second law was torturous. Could bodies exert force on each other without establishing contact? Could the gravitational force acting on an object depend on the motion of the object? How would one measure gravitational force acting on a body in motion? These are some of the pertinent questions physicists had to consider before formulating the laws of motion. There was a lot of ambiguity about the concept of force. In his famous book Principia (1687), Newton wrote that he considered forces mathematically and not physically. But later on, he was compelled to admit their physical reality, for no true physics could be constructed without them.

Newton's third law states that for every action, there is an equal and opposite reaction. That is, a force on object 1 caused by interactions with object 2 is equal and opposite to the force on object 2 caused by the interactions with object 1. The third law may appear counterintuitive at first glance. It is difficult to imagine, when a boxer hits a slender person half his weight, that he is automatically hit back with the same intensity of force (Fig. 2.2a). When a car hits a tree, the tree hits the car back with the  Figure 2.2a-c. Newton's third law states that the force of reaction is equal in magnitude and opposite in direction to the force of action. A boxer who hits an ordinary man is hit back with a force of the same intensity but opposite in direction, regardless of the size and the strength of the man (a). Two people who are arm wrestling exert on one another forces of equal magnitude but opposite direction (b). When two pendulums collide, they exert on each other forces of equal magnitude (c).

Figure 2.2a-c. Newton's third law states that the force of reaction is equal in magnitude and opposite in direction to the force of action. A boxer who hits an ordinary man is hit back with a force of the same intensity but opposite in direction, regardless of the size and the strength of the man (a). Two people who are arm wrestling exert on one another forces of equal magnitude but opposite direction (b). When two pendulums collide, they exert on each other forces of equal magnitude (c).

same intensity. When a person beats another in arm wrestling, the force he exerts on the opposing party has the same level of intensity as the force the losing party exerts on him (Fig. 2.2b). It is just that the winning party is able to continue to contract his biceps muscles while the biceps of the opposing person is yielding to the external load. The third law may be counterintuitive also because we rarely observe equality in nature—things are either bigger or smaller, heavier or lighter, and so on. Newton arrived at this counterintuitive law by considering the data on the impact of two pendulums (Fig. 2.2c). The motion of the bobs after collision could only be explained by the validity of the third law, that action is equal to reaction. Hence, the discovery that in our universe equality exists, at least within the realm of contact forces.

Magnificent structures built by men thousands of years ago suggest that ancient civilizations were at least intuitively aware of many of the subtle features of the laws of motion. However, it took many millennia for a human to state these laws in an explicit and concise manner. Greek philosophers, among them Aristotle, had attempted to formulate the physical laws of motion but they all failed. They had held to the belief that the fundamental principles of nature could be deduced only by rational thinking and not by experimentation. As a result, they did not realize that quantities such as force, velocity, and acceleration have both magnitude and direction and as such they differ fundamentally from scalar entities such as mass and temperature.

The importance of empirical observation in the discovery of physical laws was appreciated much later during the Renaissance Period by Galileo and others. It was Galileo in the seventeenth century who first formulated the parallelogram law for combining vectors such as forces acting on a particle. It was Kepler who first observed a clear illustration of Newton's third law while investigating the motion of stars. Kepler concluded that gravitational force between two stars was proportional to the mass of each star and inversely proportional to the square of the distance between them. The gravitational force had to be aligned on the straight line connecting the centers of the two stars. And, regardless of their mass, any two stars exerted on each other the same amount of force, with direction reversed. Development of calculus and vector differentiation in the seventeenth century led finally to the emergence of the branch of science that we call today classical mechanics. 