Kinetic Books – Principles of Physics Summary of Chapter 1 Chapter 1 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 = 8.756×102. 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 ma vf = vi + at Δx = vit + ½ at2 vf2 = vi2 +2aΔx Δx = ½ (vi + vf)t ss 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). When you need to do arithmetic using scientific notation, remember to deal with the leading values and the exponents separately. For multiplication, multiply the leading values and add the exponents. For division, divide the leading values and subtract the exponents. When adding or subtracting, first make sure the exponents are the same and then perform the operation on the leading values. In all cases, if the leading value of the result is not between one and 10, adjust the result. For example, 0.12×10−2 becomes 1.2×10−3. 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. c2 = a2 + b2 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) = 109 mega (M) = 106 kilo (k) = 103 centi (c) = 10–2 milli (m) = 10–3 micro (μ) = 10–6 nano (n) = 10–9 Pythagorean Theorem c2 = a2 + b2 Trigonometric functions sin θ = opposite / hypotenuse cos θ = adjacent / hypotenuse tan θ = opposite / adjacent Radian measure Angle = arc length / radius = s/ r 360° = 2π rad