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| Isaac Newton - the greatest scientist of all time |
Most of us are familiar with
Newton’s laws of motion. The three fundamental laws which govern all aspects of
movement in the universe, but lay hidden in darkness until god said ‘Let
Newton Be’ and all was light (a famous quote by Alexander Pope). Even
people who haven’t studied any science is familiar with the third law (for
every action there is an equal and opposite reaction), but we are looking
into the second law here, which, in Newton’s own words when he published it in
the Principia Mathematica in 1687 ran thus – “The alteration of
motion is ever proportional to the motive force impress'd; and is made in the
direction of the right line in which that force is impress'd”. Or, in
modern terms, change to “The acceleration a of a body is parallel and
directly proportional to the net force F acting on the body, is in the
direction of the net force, and is inversely proportional to the mass m of the
body, i.e., F = ma”. Yes, the magic equation jumps out at the end, F = ma.
Every school child knows that the
force (F) applied on a body is equal to the product of its mass (m) and the
acceleration (a) induced by the force. So much is simple. I was so inured to
the formula when Hans C Ohanian, the author of Einstein’s Mistakes shook
me to the core with the following pronouncement. “You may have been taught
in some high school or college physics course that Newton’s second law is F=ma.
If so, you were taught by an engineer, not by a real physicist. Newton himself
stated that the acceleration (or what he termed ‘the change of motion’) is
proportional to the force, not that the force is proportional to the
acceleration. Of course, both statements are true, but they differ in emphasis.
For Newton, and for most physicists, the second law expresses how the force
causes an acceleration, that is, the force is the known quantity and the
acceleration is the unknown quantity. Accordingly, physicists prefer to write
ma=F. Engineers prefer the opposite way of writing the second law, F=ma,
because for them the force is often the unknown quantity, whereas the
acceleration is the known quantity (for instance, an engineer may want to
calculate what force will be exerted on the wheels of a car when it is racing
around a curve at a known, high speed)”. (p.66 in the 2009 Norton paperback
edition). Well, it’s a lengthy tirade against engineers since we know that
engineers don’t teach school or college physics. The scale of the attack
becomes evident when we see his remarks about a prominent magazine which
praised Einstein as the engineer of the universe, in salutation to his
General Theory of Relativity which forms the basis of gravitation and the
fundamentals of space-time. Ohanian don’t let the comment go scot-free. He
immediately states that calling a physicist an engineer is no compliment!
Forgetting about the finer shades of
distinction between the two classes of professionals, if we take Ohanian’s
suggested equation ma=F for a deeper inspection, we wonder whether his
arguments would hold against common sense. To solve an algebraic equation, you
need to have the unknown quantity alone on the left-hand-side, which is not
true in this case. So, to make it ready for calculations, we have to rephrase
it as a=F/m or in a more general form as a=kF where k=1/m, the inverse of mass
– which is a meaningless physical quantity.
So what point does Ohanian try to
establish by this little trick of erudition?
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