NEWTON'S LAWS OF MOTION

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

• So far we  have considered motion of a particle in terms of the vectors r, v, and a, but we have not considered the causes of the motion.  An interaction that can cause the motion (acceleration) of an object is called a force - a push or pull on the object.  Mechanics is the study of
1. Force Laws - Which predict the forces felt by objects in particular environments, e.g. frictional force law, gravitational force law (Newton).
2. Laws of motion - Which predict how objects behave under the influence of such forces. The use of kinematics can then be used to define the details of the objects' motion.

FORCE LAWS -> LAWS OF MOTION -> KINEMATICS

We will study both force laws and laws of motion.

• 

Investigation of the effect of forces on the motion of object led Sir Isaac Newton (1642-1727)to formulate his three laws of motion.

• First Law

"In the absence of a net force acting on it, an object at rest will remain at rest and an object in motion will continue in motion at constant speed in a straight line"

When the net force on an object is zero, it does not necessarily mean there are no forces acting on the object.  Usually when the net force is zero there are several forces acting on an object which add (vectorially) to zero.

Reference frames in which Newton's 1st law is true (that is there is no net force acting on an object) are called inertial reference frames.

• Second Law

"The net force acting on an abject is equal to the product of the mass and acceleration of the object; the direction of the force is the same as that of the object's acceleration"

1. F = ma  [F_x = ma_x  ;  F_y = ma_y  ;  F_z = ma_z ]
• F - net force.

Units : Newtons  1 N = 1 kg.m/s² (SI), Pounds 1 lb = 1 slug.ft/s ²  (British)

• m - mass of object.  The standard kilogram is now (since 2018) defined in terms of Planck's constant, one of the basic physical constants of nature.  The mass which appears in the second law is called the inertial mass (as opposed to gravitational mass, defined later).  Inertia can be thought of as the reluctance of an object to change its state of rest or constant velocity motion.  All masses used to be  defined relative to the a platinum-iridium sphere kept at the International Bureau of Weights and Measures in Paris.

    Units :  kg (SI), slug (British)

• a - acceleration.  Rate of change of speed (velocity)

Units: m/s²  (SI),  ft/s²  (British)

2. Mathematically the first law is the zero acceleration special case of the second law.

• Third Law

"When an object exerts a force on another object, the second object exerts on the first a force equal in magnitude but opposite in direction"

1. Often stated, somewhat less precisely, as "Action equals Reaction"
2. Forces always appear in pairs. e.g. a book resting on a table exerts a force on the table (action), the table exerts an equal force in the opposite direction on the book (reaction).
3. Important.  Action - reaction forces act on different objects.

The importance of understanding Newton's Third Law of motion demonstrated by NASA's Gemini missions.

• We now know that Newton's "Laws" of Motion cannot be used in the realm of very large speeds (approaching the speed of light), nor at the microscopic level.  In these cases, they have been superseded by Einstein's theory of Relativity and Quantum Mechanics, respectively.  In fact, even at "normal" speeds and macroscopic scales Newton's Laws of Motion are an approximation - a very good approximation, but nevertheless an approximation.  The study of their usage is often referred to as Classical Mechanics.

• Until very recently, the kilogram was the only basic unit not defined by some property or process in nature.  As of 2018 it is now defined via an experimental procedure using a "Kibble Balance" in terms of Planck's constant (h = 6.6207004 x 10^-34 m²kg/s).  See this YouTube clip.  A complementary method via the redefinition of Avagadro's number is described in the YouTube clip - the  "World's Roundest Object".
  

• Initially, to avoid the complication of rotation, vibration and internal forces,  we will consider only the motion of "particles"- ideal objects with no extent.

• Newton's Laws set to music....  Try these
• Taylor Swift "Cover"
• Heavy Metal Newton
• Newton's Rap
  

“When I was a boy of 14, my father was so ignorant I could hardly stand to have the old man around. But when I got to be 21, I was astonished at how much the old man had learned in 7 years”

Mark Twain

Dr. C. L. Davis

Physics Department

University of Louisville

email: c.l.davis@louisville.edu