Conceptual Physics

1.17 - Summary

Scientists use the Système International d’Unités, also known as the metric system
of measurement. Examples of metric units are meters, kilograms, and seconds.

In these systems, units that measure the same property, for example units for mass,
are related to each other by powers of ten. Unit prefixes tell you how many powers
of ten. For example, a kilogram is 1000 grams and a kilometer is 1000 meters, while
a milligram is one one-thousandth of a gram, and a millimeter is one-thousandth of
a meter.

Numbers may be expressed in scientific notation. Any number can be written as a
number between 1 and 10, multiplied by a power of ten. For example,
875.6 = 8.756×10^2.

A standard is an agreed-on basis for establishing measurement units, like defining
the kilogram as the mass of a certain platinum-iridium cylinder that is kept at the
International Bureau of Weights and Measures, near Paris. A physical constant is
an empirically measured value that does not change, such as the speed of light.

In the metric system, the basic unit of length is the meter; time is measured in
seconds; and mass is measured in kilograms.

Sometimes a problem will require you to do unit conversion. Work in fractions so
that you can cancel like units, and make sure that the units are of the same type (all
are units of length, for instance).

The Pythagorean theorem states that the square of the hypotenuse of a triangle is
equal to the sum of the squares of the two legs.

c^2 = a^2 + b^2

Trigonometric functions, such as sine, cosine and tangent, relate the angles of a
right triangle to the lengths of its sides.

Radians (rad) measure angles. The radian measure of an angle located at the
center of a circle equals the arc length it cuts off on the circle, divided by the radius
of the circle.

Prefixes

giga (G) = 10^9

mega (M) = 10^6

kilo (k) = 10^3

centi (c) = 10–2

milli (m) = 10–3

micro (ȝ) = 10–6

nano (n) = 10–9

Pythagorean Theorem

c^2 = a^2 + b^2

Trigonometric functions

sinș= opposite / hypotenuse

cosș= adjacent / hypotenuse

tanș= opposite / adjacent

Radian measure

Angle = arc length / radius =s/r

360° = 2ʌrad

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