"Annenberg Media" "¶" "FORCE= MASS TIMESACCELERATION." "MECHANICS, THESCIENCEOF MOTION," "CANBESUMMARIZED INTHATONEEQUATION" "F= ma." "ITISTHEHEART OFCLASSICALMECHANICS." "IN 1543, COPERNICUS WROTE THIS LITTLE BOOK," "AND THE ARISTOTELIAN WORLD STARTED COMING UNGLUED." "150 YEARS LATER," "IT STILL LAY IN RUINS," "AND THERE WAS NOTHING" "TO TAKE ITS PLACE." "OF COURSE, SOME PROGRESS HAD BEEN MADE." "KEPLER HAD DISCOVERED HIS THREE LAWS." "FALLING BODIES WERE UNDERSTOOD, AND SO WAS INERTIA." "BUT THERE WAS NO UNIFYING PRINCIPLE." "THE SEAMLESS PERFECTION OF THE ARISTOTELIAN WORLD" "HAD TURNED TO BUZZING CONFUSION." "THEN, IN ONE BREATHTAKING BOOK," "ISAAC NEWTON INVENTED PHYSICS AS WE KNOW IT TODAY" "AND RESTORED ORDER TO THE HEAVENS AND THE EARTH." "WHEN TRYING TO DESCRIBE" "THE BASIC MACHINERY OF THE WORLD," "A NATURAL QUESTION IS..." "[GUNSHOT]" "WHERE TO BEGIN." "ISAAC NEWTON BEGAN WITH THREE FUNDAMENTAL PRINCIPLES" "NEWTON'S LAWS." "WITH THE INCREDIBLE SPEED AND ELEGANCE" "OF UNLEASHED GENIUS," "HE EXPLAINED THE MOTION OF ALMOST EVERYTHING" "ON AND ABOVE THE SURFACE OF THE EARTH." "REFINED TO THEIR ESSENCE," "NEWTON'S THREE LAWS ARE ONE PROFOUNDLY POWERFUL EQUATION." "FORCE = MASS TIMES ACCELERATION." "UNDERSTAND THAT EQUATION" "WHAT IT MEANS AND HOW TO USE IT" "AND IT'S POSSIBLE TO UNDERSTAND THE MECHANICAL UNIVERSE." "AT THE SAME TIME," "UNDERSTAND THAT CONSIDERABLE COMPLEXITY" "CAN RESIDE IN WHAT APPEARS TO BE PURE AND SIMPLE." "FOR EXAMPLE, A CLOSER LOOK AT F = ma" "IMMEDIATELY REVEALS TWO COMPLICATIONS" "FIRST," "F = ma IS A VECTOR EQUATION." "BOTH FORCE AND ACCELERATION ARE VECTORS." "IN OTHER WORDS, THEY HAVE DEFINITE DIRECTIONS." "IN F = ma, THEY MUST HAVE THE SAME DIRECTION." "THE SECOND COMPLICATION" "ARISES IN THE SYMBOL a FOR ACCELERATION." "REMEMBER, ACCELERATION ISN'T THE POSITION OF SOMETHING," "AND IT'S NOT HOW FAST SOMETHING CHANGES ITS POSITION." "ACCELERATION IS HOW FAST SOMETHING GETS FASTER." "SO ACCELERATION IS THE DERIVATIVE OF A DERIVATIVE," "AND ISAAC NEWTON'S SIMPLE EQUATION, F = ma," "IS A VECTOR EQUATION" "ABOUT A DERIVATIVE OF A DERIVATIVE." "FOR EXAMPLE..." "WHEN A BODY, OR A MASS, FALLS," "GRAVITY EXERTS A FORCE, F" "FORCE IN THE DOWNWARD DIRECTION, OF COURSE" "AND THE RESULT IS ACCELERATION." "SO THERE IT IS" "F = ma" "ACCELERATION AND FORCE IN THE SAME DIRECTION." "COMPLICATED YET BEAUTIFUL IN ITS SIMPLICITY." "THAT'S THE WELL-KNOWN EQUATION." "NOW, IN THE CASE OF A FALLING BODY," "WHAT'S KNOWN ABOUT ACCELERATION?" "IT'S CONSTANT, FOR ONE THING." "AND FOR ANOTHER," "IT'S THE SAME FOR ALL FALLING BODIES." "AND WHAT'S MORE, IT'S CALLED g." "THE FORCE OF GRAVITY..." "ON EVERY FALLING BODY" "= ITS MASS TIMES THE ACCELERATION, g," "IN THE DOWNWARD DIRECTION." "BUT THIS EQUATION ALSO DESCRIBES MOTION" "FOR OTHER THAN THE DOWNWARD DIRECTION." "GRAVITY EXERTS THE SAME FORCE ON A BODY," "NO MATTER WHICH DIRECTION THAT BODY TRAVELS." "YEAH!" "YEAH!" "ONCE AN OBJECT IS IN MOTION" "ASIDE FROM AIR RESISTANCE" "GRAVITY IS THE ONLY FORCE ACTING ON IT," "WHETHER DROPPED FROM A TOWER," "SHOT FROM A TOWERING MOUNTAIN..." "OR HEAVED BY A TOWERING MOUNTAIN OF A MAN." "MEASURE." "ALL MOVING OBJECTS FALL UNDER THE INFLUENCE OF GRAVITY." "AN EQUATION THAT EXPLAINS" "THE PATH OF ANY PROJECTILE ON EARTH" "IS POWERFUL INDEED." "AND TO SEE HOW IT REALLY WORKS..." "[GUNSHOT]" "IT'S NECESSARY TO GO BACK TO THE BEGINNING." "WITH HIS FIRST LAW," "NEWTON EMBRACED THE IDEA OF INERTIA." "HE WROTE, "EVERY BODY CONTINUES IN ITS STATE OF REST" ""OR OF UNIFORM MOTION IN A STRAIGHT LINE," ""UNLESS IT IS COMPELLED TO CHANGE THAT STATE" "BY FORCES IMPRESSED UPON IT."" "INERTIA WAS AN IDEA" "THAT NEWTON INHERITED FROM GALILEO." "IT WAS AN EXTRAORDINARY IDEA" "THAT IF ILLUSTRATED WITH MODERN IMAGES" "GOES SOMETHING ALONG THESE LINES" "ONCE A BODY IS IN MOTION," "IT NATURALLY CONTINUES IN A STRAIGHT LINE" "UNLESS INFLUENCED BY SOME FORCE." "NEWTON'S SECOND LAW" "INDICATES EXACTLY HOW A FORCE CHANGES THE MOTION OF AN OBJECT." "AS NEWTON EXPLAINED IT," ""THE CHANGE IN MOTION" ""IS PROPORTIONAL TO THE FORCE IMPRESSED." ""IT IS MADE IN THE DIRECTION OF THE STRAIGHT LINE" "IN WHICH THE FORCE IS IMPRESSED."" "[GUNSHOT]" "NEWTON USED THE WORD MOTION TO MEAN MOMENTUM" "THE VELOCITY OF A BODY MULTIPLIED BY ITS MASS." "WHILE NEWTON EXPRESSED HIMSELF WITH CLASSICAL GEOMETRY" "USING GEOMETRIC FIGURES AND RATIOS BETWEEN QUANTITIES," "HE KNEW HIS LAWS" "COULD BE EXPRESSED AS DIFFERENTIAL EQUATIONS." "NEWTON'SSECONDLAW SAYS THAT THE IMPRESSED FORCE" "ISEQUALTO THERATEOFCHANGE OFMOMENTUM." "FORA BODYWITHCONSTANTMASS ," "THIS DIFFERENTIAL EQUATION REDUCESTO" "FORCE= MASS TIMESACCELERATION" "F= ma." "TO EVERY ACTION..." "THERE IS ALWAYS AN EQUAL REACTION." "OR, THE MUTUAL ACTIONS OF TWO BODIES UPON EACH OTHER" "ARE ALWAYS EQUAL AND DIRECTED TO CONTRARY PARTS." "THIS IS NEWTON'S THIRD LAW." "SOMETHING CANNOT TOUCH SOMETHING ELSE" "WITHOUT BEING TOUCHED IN RETURN." "IN OTHER WORDS, BODIES DON'T MERELY ACT." "THEY INTERACT WITH ONE ANOTHER." "AT THE SAME TIME," "ALL THREE OF NEWTON'S LAWS" "ACT AND INTERACT THROUGHOUT THE PHYSICAL WORLD." "THE TRAJECTORY OF ANY PROJECTILE," "IN A POWERFUL AND MOVING FASHION," "DEMONSTRATES THE CONSEQUENCES OF NEWTON'S THREE LAWS." "WHEN AN OBJECT IS LAUNCHED" "AND ALLOWED TO TRAVEL FREELY," "WHAT'S THE NATURE OF ITS TRAJECTORY?" "NO MATTER WHAT THE PROJECTILE AND ITS PURPOSE," "COULD IT BE THAT ALL TRAJECTORIES" "ARE ESSENTIALLY THE SAME?" "UNDERSTANDING THE COURSE OF ANY PROJECTILE" "ARISES FROM AN INSIGHT INTO THE LAWS" "THAT GOVERN FORCE AND MOTION." "ONE FELLOW CREDITED EARLY ON WITH SUCH AN INSIGHT" "AND FIRST-HAND KNOWLEDGE ABOUT PROJECTILES" "WAS DAVID," "WHO IS REMEMBERED FOR HIS LEGENDARY CONFRONTATION" "WITH GOLIATH." "AGAINST CONSIDERABLE ODDS, YOUNG DAVID DEMONSTRATED" "THE RELATIONSHIP BETWEEN FORCE AND MOMENTUM." "ACTUALLY, DAVID AND GOLIATH" "MIGHT NOT HAVE BEEN QUITE AS MISMATCHED" "AS LEGEND PORTRAYS THEM." "AFTER ALL, IS THIS THE MODEL OF DEVASTATING INTELLECT?" "IN ANY CASE," "DAVID MANAGED TO DEMONSTRATE FORCE AND MOMENTUM EXPERTLY" "AND WITHOUT THE HELP OF ARISTOTLE, MUCH LESS NEWTON." "GOLIATH GOT THE POINT." "NOT ONLY THAT" "HE ROUTINELY OBEYED THE LA/@OF GRAVITY" "ANOTHER PHENOMENON THAT WORKED PERFECTLY" "LONG BEFORE IT WAS UNDERSTOOD." "NEWTON'S LAWS DIDN'T CHANGE THE WAY THE WORLD WORKS," "BUT THEY CHANGED FOREVER" "THE WAY IN WHICH IT'S UNDERSTOOD." "WHETHER IT'S ON A FIELD OF BATTLE," "AN ATHLETIC FIELD," "OR THE GREEN FIELDS OF ENGLAND," "THE PATH OF ANY PROJECTILE" "CAN BE DESCRIBED IN THE FIELD OF MATHEMATICS." "IN NEWTON'S WORDS, "THEN FROM THESE FORCES" ""I DEDUCED THE MOTIONS OF THE PLANETS," "THE COMETS, THE MOON, AND THE SEA."" "NEWTON WASN'T THE FIRST TO PONDER THE PATH" "OF A FLYING OBJECT ON EARTH OR IN THE HEAVENS," "BUT HE STOOD ALONE IN HIS KNOWLEDGE" "THAT THE SAME LAWS GOVERN THE COURSE OF BOTH." "LONG BEFORE NEWTON," "GALILEO GALILEI DESCRIBED PROJECTILE MOTION PERFECTLY." "HE REALIZED BODIES CAN FALL VERTICALLY" "AND MOVE HORIZONTALLY" "AT THE SAME TIME." "FROM GALILEO'S POINT OF VIEW," "WHICH TOOK IN EVERYTHING FROM THE HEAVENS" "TO THE HEAVENLY GARDENS OF THE RENAISSANCE," "A BODY'S MOTION HAS TWO COMPONENTS" "INDENDENT OF EACH OTHER." "GALILEO'S EXTRAORDINARY VISION" "IS EXPLAINED BY ISAAC NEWTON'S EXTRAORDINARY EQUATION." "THEVERTICALCOMPONENT OFTHEVECTORFORCE" "ISmgDOWNWARD," "OR- mg." "NOFORCEAT ALLACTS IN THE HORIZONTAL DIRECTION." "ONLY THE VERTICAL COMPONENT OFACCELERATIONIS -g ." "IN THE HORIZONTAL DIRECTION, WHERE THERE IS NO FORCE," "THEACCELERATIONIS 0." "ACCELERATION IS THE RATE OFCHANGEOF SPEED." "SINCE THE HORIZONTAL SPEED ISNOTCHANGING," "ITMUSTBE CONSTANT" "CONSTANTSPEED IN THE HORIZONTAL DIRECTION" "ANDCONSTANT ACCELERATIONDOWNWARD" "BOTH ACTING INDEPENDENTLY ANDSIMULTANEOUSLY." "THESE ARE THE ELEMENTS OF GALILEO'S TRAJECTORIES..." "AND THEY'RE ALSO THE RESULTS OF NEWTON'S EQUATION," "FORCE = MASS TIMES ACCELERATION" "F = ma." "BUT TO UNDERSTAND THE ONGOING SIGNIFICANCE" "OF F = ma," "IT'S NECESSARY TO RETURN TO A TIME" "BEFORE SCHOLARS HAD ITS HELP" "IN GRAPPLING WITH WORLDLY PHENOMENA." "IN ANCIENT GREECE, SCHOLARS BELIEVED" "THAT EVERYTHING IN NATURE CAME TO REST," "THAT COMING TO REST" "WAS THE NATURE OF ALL MOVING THINGS." "ACCORDING TO THE ARISTOTELIANS," "ALL MOVING OBJECTS WERE PROPELLED BY A MOVER." "WHEN THE MOVER COULDN'T BE SEEN," "AS IN PROJECTILE MOTION," "ARISTOTLE SAID THAT AIR ITSELF" "WAS RESPONSIBLE FOR THE MOVEMENT." "MUCH LATER, EVEN THOUGH EUROPE IN THE MIDDLE AGES" "RETAINED THE ARISTOTELIAN WORLD VIEW," "THAT EXPLANATION WASN'T ENTIRELY SATISFACTORY." "TO EXPLAIN THE UNESCORTED MOTION OF PROJECTILES" "SUCH AS SPEARS, ARROWS, AND CANNONBALLS," "SCHOLARS CAME UP WITH THE IDEA OF IMPETUS." "LAUNCHING A PROJECTILE" "IMBUED IT WITH A FINITE AMOUNT OF IMPETUS," "WHICH GAVE THE OBJECT ITS MOTION." "WHEN ITS IMPETUS WAS CONSUMED," "THE OBJECT" "SUDDENLY DROPPED TO EARTH." "IMPETUS WASN'T A BAD IDEA," "BUT IT FELL SHORT OF ITS TARGET." "THE MEDIEVAL IDEA OF IMPETUS" "FELL JUST SHORT" "OF THE PRINCIPLE OF INERTIA," "WHICH WASN'T HIT UPON" "UNTIL THE RENAISSANCE," "WHEN THE PARABOLIC PATH" "OF A REAL PROJECTILE" "WAS DISCOVERED BY GALILEO." "IN GALILEO'S WORDS, "IT HAS BEEN OBSERVED" ""THAT MISSILES AND PROJECTILES" ""DESCRIBE A CURVED PATH OF SOME SORT." ""HOWEVER, NO ONE HAS POINTED OUT THE FACT" "THAT THIS PATH IS A PARABOLA."" "WITH SUCH INSIGHT, GALILEO WAS LIVING TO SEE" "THE 2,000-YEAR REIGN OF THE ARISTOTELIAN WORLD VIEW" "COME TO AN END." "AND HE WASN'T ALONE." "ABOUT THE SAME TIME," "JOHANNES KEPLER," "CHRISTIAN HUYGENS IN THE NETHERLANDS," "AND RENE DESCARTES IN FRANCE" "AND OTHERS ALSO BEGAN TO SEE THE UNIVERSE WITH NEW EYES." "AS EXTRAORDINARY AS THIS COLLECTION OF SCIENTISTS WAS," "THEIR INDIVIDUAL VIEWPOINTS OVERLOOKED SOMETHING" "A SYNTHESIS" "AN ORGANIZING PRINCIPLE" "FOR THE PHYSICAL WORLD AS A WHOLE." "IT WOULD TAKE EXTRAORDINARY CIRCUMSTANCES" "TO EXPLAIN THE WORLD." "IT WOULD REQUIRE THE RIGHT PERSON" "IN THE RIGHT PLACE AT THE RIGHT TIME." "THE RIGHT TIME WAS 1665." "AND THE RIGHT PERSON WAS ISAAC NEWTON." "AT ONLY 23 YEARS OF AGE," "NEWTON CONCEIVED THE DISCOVERIES" "THAT WOULD ALTER FOREVER" "THE WORLD'S UNDERSTANDING OF THE UNIVERSE." "WITH JUST THREE FUNDAMENTAL LAWS," "NEWTON GAVE MOTION A CAUSE," "AND IN DOING SO, HIS DYNAMIC PRINCIPLE" "COMPLETED GALILEO'S MATHEMATICAL DESCRIPTION OF MOTION." "IN OTHER WORDS," "WHILE GALILEO'S KINEMATICS DESCRIBED MOTION," "NEWTON'S DYNAMICS EXPLAINED IT." "BUT NEWTON'S LAWS ALSO EXPLAIN HOWA BODYMOVES." "BY COMBINING HIS CALCULUS WITH HIS MECHANICS," "THE MOTION OF A MOVING OBJECT CAN BE DESCRIBED PERFECTLY." "THE MOTION OF A PROJECTILE" "HASANACCELERATION EQUALTO-g" "INTHEVERTICALDIRECTION" "ANDA CONSTANTSPEED IN THE HORIZONTAL DIRECTION." "AND WHAT'S THE MEANING OF THAT CONSTANT?" "THE FORCE BEHIND THIS OBJECT'S PROPULSION" "COMES FROM THE THRUST OF THE ATHLETE'S TORSO." "THIS FORCE LASTS ONLY A MOMENT" "AND DETERMINES THE SHOT'S INITIAL SPEED." "WHEN THE SHOT LEAVES THE HAND," "IT HAS SOME COMPONENT OF VELOCITY IN THE X DIRECTION," "WHICH IS THE CONSTANT VALUE THE HORIZONTAL SPEED HAS" "AND WILL CONTINUE TO HAVE THROUGHOUT ITS JOURNEY" "UNTIL IT HITS THE GROUND." "HOWEVER, THE VERTICAL COMPONENT OF VELOCITY" "IS CHANGING AT A RATE EQUAL TO -g." "THE DERIVATIVE OF VERTICAL SPEED WITH RESPECT TO TIME" "IS -g, NOT ZERO." "WHAT FUNCTION HAS THE DERIVATIVE -g?" "gt IS ONE ANSWER." "BUT -gt + ANY CONSTANT IS ALSO AN ANSWER," "SINCE THE DERIVATIVE OF A CONSTANT IS ZERO." "WHAT'S THE MEANING OF THE CONSTANT?" "IT'S THE VERTICAL SPEED THE OBJECT STARTS OUT WITH," "EVEN IF IT STARTS OUT WITH A BANG." "PRETEND FOR A MOMENT THAT THERE IS NO GRAVITY." "THEN ANY PROJECTILE WOULD FOLLOW A STRAIGHT-LINE PATH" "WITH BOTH THE HORIZONTAL AND THE VERTICAL SPEED" "WITH WHICH IT STARTED OUT." "BUT GRAVITY DOES SHAPE THE MOTION OF A PROJECTILE." "AND HOW IT DOES" "IS EXPRESSED IN GALILEO'S LAW OF FALLING BODIES." "A PROJECTILE CONTINUALLY FALLS" "BENEATH ITS IMAGINARY STRAIGHT-LINE PATH" "AT A RATE EQUAL TO 1/2 gt-SQUARED," "JUST AS IF IT WERE DROPPED FROM REST." "ALL THESE HARD-EARNED INSIGHTS OF GALILEO" "ARE THE SIMPLE AND DIRECT CONSEQUENCES" "OF ISAAC NEWTON'S ONE CONCISE LAW," "SUMMARIZED IN THE EQUATION F = ma." "I'VE GOT ANOTHER DAVID AND GOLIATH STORY." "NATURALLY, I'M DAVID." "AND THERE'S GOLIATH, HANGING FROM A TREE." "BUT THIS TIME, INSTEAD OF A SLING," "I'LL GET HIM WITH A SOPHISTICATED PROJECTILE" "THIS ONE." "BUT THE MOMENT I PULL THE TRIGGER," "HE'LL GET FRIGHTENED AND LET GO OF THE TREE." "SO HE'S GOING TO BE FALLING." "HOW MUCH DO I HAVE TO LEAD HIM BY" "IN ORDER TO HIT HIM?" "I'LL FIND THE ANSWER THE WAY ANY GREAT HUNTER WOULD" "I'LL WRITE THE EQUATIONS OF THE PROJECTILE." "WE NEED TO KNOW Z AND X." "WHAT WE KNOW INSTEAD IS dz/dt" "BECAUSE THAT'S JUST Vz" "= -gt + Vz NAUGHT." "AND dx/dt" "BECAUSE THAT'S JUST Vx" "= Vx NAUGHT." "1/2 gt-SQUARED." "NOW, WITHOUT THE EFFECT OF GRAVITY," "THESE WOULD BE THE EQUATIONS OF A STRAIGHT LINE." "IT WOULD BE A STRAIGHT LINE FROM THE GUN BARREL" "TO THE POINT IT'S AIMED AT." "THE EFFECT OF GRAVITY IS TO MAKE THE MISSILE" "FALL BELOW THAT STRAIGHT LINE" "BY AN AMOUNT EQUAL TO 1/2 gt-SQUARED," "SO THE ACTUAL TRAJECTORY LOOKS LIKE THAT." "BUT THAT'S EXACTLY THE DISTANCE THE MONKEY WILL FALL." "HE'LL FALL JUST THE SAME 1/2 gt-SQUARED" "AND MEET THE MISSILE IN MIDAIR." "THAT'S WHAT WE WANT TO DO." "WE WANT TO AIM THE MISSILE DIRECTLY AT THE MONKEY." "NOW I'LL SHOOT DOWN THAT MONKEY." "SOMEONE IS BOUND TO ASK WHY I WOULD SHOOT A MONKEY." "DON'T ASK." "THIS ISN'T ETHICS, IT'S PHYSICS." "YOU CAN SEE THAT THE LASER BEAM" "PASSES BY THE SIGHTS OF THE GUN" "AND IT HITS THE MONKEY." "NOW I'LL LOAD UP MY MISSILE LAUNCHER." "NOW WE'RE READY TO SHOOT HIM." "I'VE PRACTICED THIS DEMONSTRATION MANY TIMES." "IN THE HUNDREDS OF TIMES I'VE DONE THIS DEMONSTRATION," "I HAVE NEVER ONCE HIT THAT MONKEY." "THAT'S WHY HE KEEPS VOLUNTEERING." "WE'RE GOING TO DO IT NOW." "EVERYBODY READY?" "HERE WE GO." "AAH!" "[APPLAUSE]" "WE GOT HIM." "THAT MAY BE THE FIRST TIME" "A MONKEY HAS EVER BEEN SHOT DOWN BY AN EQUATION." "BUT WHAT AN EQUATION!" "IF YOU ASK THE AVERAGE PHYSICIST" "WHAT IS THE MOST IMPORTANT SINGLE EQUATION" "IN ALL OF PHYSICS," "YOU'D PROBABLY GET F = ma." "YET THERE'S SOMETHING VERY MYSTERIOUS" "ABOUT THAT EQUATION." "IT HAS JUST THREE QUANTITIES-- FORCE, MASS, AND ACCELERATION." "WE PRETTY WELL UNDERSTAND WHAT ACCELERATION MEANS," "BUT WHAT EXACTLY IS FORCE?" "AND WHAT DO WE MEAN BY MASS?" "ONE WAY TO FIND OUT IS TO USE THIS EQUATION." "THAT'S WHAT WE'VE DONE TODAY IN THE CASE OF GRAVITY." "WE FOUND OUT NOTHING ABOUT THE NATURE OF GRAVITY," "BUT WE USED THIS EQUATION" "TO TELL US THE FORCE ACTING ON A BODY." "IF WE KNOW A BODY'S MASS" "AND WE OBSERVE ITS ACCELERATION," "WE CAN FIND THE FORCE ON IT." "BUT WITHOUT THIS EQUATION," "WE DON'T KNOW THE MASS OF A BODY." "WITHOUT KNOWING THE MASS OF THE BODY," "THE EQUATION MEANS NOTHING AT ALL." "SO IS THE MOST IMPORTANT SINGLE EQUATION IN PHYSICS" "A MEANINGLESS LOGICAL ABSURDITY?" "THIS IS A PROBLEM PHILOSOPHERS HAVE DEBATED" "FOR OVER 300 YEARS." "YET ONE THING IS CLEAR." "BEFORE ISAAC NEWTON WROTE THIS EQUATION DOWN," "THE WORLD WAS ONE OF BUZZING CONFUSION." "AFTER HE WROTE IT DOWN," "THE WORLD BECAME ORDERLY, COMPREHENSIBLE, AND PREDICTABLE." "SO WHATEVER ELSE THIS EQUATION IS," "IT CERTAINLY ISN'T MEANINGLESS." "THE ONLY WAY TO UNDERSTAND WHAT THIS EQUATION IS ABOUT" "IS BY USING IT." "THAT'S WHAT THE REST OF OUR STORY IS ABOUT." "FORCE= MASS TIMESACCELERATION." "MECHANICS, THESCIENCEOF MOTION," "CANBESUMMARIZED INTHATONEEQUATION" "F= ma." "CAPTIONING PERFORMED BY THE NATIONAL CAPTIONING INSTITUTE, INC." 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