Physics: The First Science

By Peter Lindenfeld; Suzanne White Brahmia | Go to book overview

CHAPTER 2

Some Tools of the Trade:
Numbers, Quantities, and Units
The language of physics: symbols and formulas
Positive and negative numbers
Zero
Numbers, huge and tiny: powers of 10
Precision: Significant figures
Quantities and units
Ratios and proportional reasoning
Tables, graphs, equations, and functions
Right-angled triangles
Once more the four forces, this time quantitatively
The gravitational force
The electric force
The other forces

So far we have used words, almost exclusively. We have talked about size, force,
and energy, but mostly without using numbers, although a few times they almost
forced themselves on us. But most of the time we have to know how big a
distance is, or a force, or any other quantity, and that requires numbers and
units. We also want to describe relations between different quantities, and do
that with symbols, such as E for energy, and M for mass.

All of that is mathematics. Mathematics is the language in which the ideas,
facts, and relationships of physics are best expressed. Sometimes it’s just short-
hand. It is much easier to write v = 32 m/s than “the velocity is thirty-two meters
per second,” or

, rather than “the average velocity of an object is equal
to the displacement along the x-axis divided by the time it took to make that
displacement.”

Sometimes the relationships are more complex, like F = Ma: “the force, or,
if there is more than one, the sum of all the forces acting on an object, is equal
to the mass of the object multiplied by its acceleration.”

You can see that just as a way of writing things down in shorthand notation
with symbols like v and x, math is very helpful. But it does more than that. It
lets us write down relationships between different quantities, and change them
so that they lead to other relationships. To do the same with words would be
cumbersome even for the simplest ones, and close to impossible for others.

-16-

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