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(16) Newton's Laws of Motion
1.   Force and Inertia


13. Free Fall

14. Vectors

15. Energy

16. Newton's Laws

17. Mass

17a. Measuring Mass
        in Orbit
17b. Inertial balance

18. Newton's 2nd Law

18a. The Third Law
 Isaac Newton

Isaac Newton was born in 1642, the year Galileo died. Almost all his creative years were spent at the University of Cambridge, England, first as a student, later as a greatly honored professor. He never married, and his personality continues to intrigue scholars to this day: secretive, at times cryptic, embroiled in personal quarrels with some scholars yet generous to others, bestowing his attention not just on physics and mathematics, but also on religion and alchemy.

The one thing about which everyone agrees is his brilliant talent. Three problems intrigued scientists in Newton's time: the laws of motion, the laws of planetary orbits, and the mathematics of continuously varying quantities--a field nowadays known as [differential and integral] calculus. It may be fairly stated that Newton was the first to solve all three. No wonder that the poet Alexander Pope, who lived in Newton's time, wrote:

      Nature and Nature's laws lay hid in night
      God said:"Let Newton be!" and all was light.

        "Newton's three Laws of Motion" are the foundation of the theory of motion--e.g., of orbits and rockets.
        This section discusses two concepts on which they are based:
Force     and     Inertia

For later reference, Newton's three laws are listed below the way they are usually formulated :

  1. In the absence of forces, ("body") at rest will stay at rest, and a body moving at a constant velocity in a straight line continues doing so indefinitely.

  2. When a force is applied to an object, it accelerates. The acceleration a is in the direction of the force and proportional to its strength, and is also inversely proportional to the mass being moved. In suitable units:

    a = F/m

    or in the form usually found in textbooks

    F = m a

    More accurately, one should write

    F = ma

    with both F and a vectors in the same direction (denoted here in bold face). However, when only a single direction is understood, the simpler form can also be used.

  3. "The law of reaction," sometimes stated as "to every action there exists an equal and opposite reaction." In more explicit terms:

    Forces are always produced in pairs, with opposite directions and equal magnitudes. If body #1 acts with a force F on body #2, then body #2 acts on body #1 with a force of equal strength and opposite direction.

However... "to own a concept," you need to go beyond formal definitions and get an intuitive idea of what it means. Science often develops like this, too. You start with an improvised "working definition," then when you understand it better, you replace it with a more precise meaning. That approach is used here. Explanations may be longer--but the process is easier on the student and avoids the frustration of prematurely introduced concepts..    

The concept of Force

  As a working definition, let us call "force" that which causes or changes motion.

  One force everyone is familiar with is the weight of objects, the force which tries to make them move downwards, to fall towards the center of the Earth. We may thus measure force (at least now, temporarily) in kilograms of weight, and view as force anything that can be matched by weight. For instance, a spiral spring can be compressed or stretched by weight, so it is fair to say that it, too, exerts a force when compressed or stretched.

  Based on hindsight--on experience with forces noted by many people, including Newton--we may distinguish two basic situations in which force creates motion:

  1. The force moves an object overcoming external resistance.
  2. The force moves an object against negligible external resistance.

1. Motion against Outside Resistance

  This kind of motion will be discussed in a later section, in connection with the concept of "work." Examples include:
  • --Lifting a book from the floor to the table (the force produced by the hand doing the lifting must overcome the downward pull of gravity)
  • --Dragging a table across the room (the pull of your hand must overcome the friction of the floor),
  • --An airliner flying at 600 mph (the thrust of its engines overcomes air resistance)
The speed of the motion does not enter here, so in principle it can even cover the case when the opposing force completely balances the applied one, resulting in no motion at all
  • --A table stands on the floor, without moving. The downward force of the weight of the table encounters resistance by the floor, which does not allow it to move any further downwards. The downward velocity is zero and the forces are balanced or "in equilibrium."

2. Motions Without Significant Resistance

  It was Newton's insight that in the absence of external resistance, motions in a straight line and at constant speed would continue indefinitely. No force is necessary. That is Newton's first law of motion:

    " In the absence of external forces, motion in a straight line and at constant speed continues indefinitely. "

  A hockey puck sliding on a sheet of ice can travel great distances, and the smoother the ice, the further it goes. Newton realized that what ultimately stopped such motions was the friction of the surface. If an ideally smooth ice could be produced, with no friction at all and extending to unlimited distances, the puck would continue indefinitely, never stopping, in the same direction and with the same velocity as the ones with which it had started.

What a force can do in the absence of resistance is increase the velocity of an object --  accelerate it.  

However... even without external resistance, there remains an internal resistance, by the object itself. An astronaut pushing a one-ton satellite out of the cargo bay of the space shuttle quickly finds that even though the satellite seems "weightless," it is not easily moved. Given a push by the astronaut, it will indeed start to move, but v-e-r-y   v-e-r-y   s-l o-w-l-y . It resists being put in motion, and once moving, it resists just as much being slowed down or stopped.

Newton named that internal resistance inertia.

  Obviously, inertia increases with the amount of matter. A bowling ball is harder to get moving and harder to stop than a hollow rubber ball of the same size.

  The bowling ball is also heavier, that is, it is pulled downward with greater force: but weight is an effect of gravity, while inertia is not. The two seem to go together in some way, and the next section examines this further.


  Supertankers (" Large Crude Carriers") are large ships which can carry 150-300,000 tons of crude oil, at about 18 mph (nearly 30 km/h). Such a heavy load carries an enormous inertia. Even with the engine thrown into reverse, supertankers take a mile or more to come to a stop, and are equally hard to turn around. Yet a wreck must be avoided at all costs, because oil spills cause enormous ecological damage.

  Supertanker officers are therefore trained in a facility in the Netherlands (Holland), piloting a small replica of a supertanker around a lake. The replica is about 25 feet long, and the officer sits in it with just the head showing. Although small, the boat is heavy and underpowered. It only has a small engine, the size of an outboard engine used by small boats, and its rudder is also to scale, small. Therefore, even though the boat has far less speed than a supertanker, it is also hard to stop and control (in the limited space of the lake), and can therefore train officers in the handling of heavily loaded ships.

Exploring Further

list of web links related to Isaac Newton, his life and work.

  The portrait of Newton at the start of this section, perhaps his best likeness, was painted in 1689 by Godfrey Kneller, and for 150 years its existence was known only to a few. For its story and for some other paintings of the man, see " Images of Newton, " Endeavour, 24 p. 51-52, No. 2, 2000.

Next Stop: #17 Mass

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Author and Curator:   Dr. David P. Stern
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Last updated: 10-9-2004
Reformatted 24 March 2006