TY Physics Measurement Module 1

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1 TY Physics Measurement Module 1 Introduction Units of measure were among the earliest tools invented by humans, they were needed for many tasks, such as constructing dwellings, fashioning clothes, or bartering food and raw materials. A unit of measurement is a standardised quantity of a physical property. The earliest known systems of weight and measures used parts of the body and the natural surroundings as measuring instruments. Thus, units of measure could vary not only from location to location, but also from person to person. An important feature of modern systems is standardisation, with each unit having a universally recognised size. A number of metric systems have evolved since the adoption of the original metric system in France in The current system is the International System. Quantities and Units Physical quantities are such things as mass and force. All have to be measured in some way and each has its own unit. These are chosen by agreement and are called SI units (abbreviated from the French Système International). All quantities are classified as either basic quantities or derived quantities. Basic quantities Basic quantities are a set of quantities from which all other quantities are derived. Each quantity has is own SI unit. Mass Basic quantity Symbol Basic SI unit Abbreviation Mass m kilogram kg Length l metre m Time t second s Current I ampere A temperature T kelvin K Quantity of a substance - mole mol Luminous intensity - candela cd Since 1889, the SI system defines the magnitude of the kilogram to be equal to the mass of the International Prototype Kilogram (IPK), right-circular alloy cylinder (90% Platinum/10% iridium).the standard kilogram is the only SI unit to still be defined in terms of a real artefact. All other SI Units are now defined in terms of fundamental constants.

2 Length The meter is a measure of length. Historically, the meter was defined as 1/10,000,000 of the distance from the equator to the North pole through Paris. Today, it is defined as the distance travelled by light in an absolute vacuum in 1/299,792,458 of a second. Decimal multiples and submultiples of the metre, include kilometre (1000m), centimetre (1/100 m). Time The unit of time is the second (s) and is quantified as the duration of exactly 9,192,631,770 periods of the radiation emitted from caesium-133 at a temperature of 0 o K. Current The SI unit of current the ampere is defined as being equal to the size of the current flowing though parallel, infinitely long, straight wires in a vacuum that produce a force between the wires of 2 x 10-7 N every metre. Temperature The SI unit for temperature is the Kelvin. It is equal to 1/ of the temperature of the triple point of water (the point at which, ice, water and steam can exist at the same time) on the absolute scale. Quantity of a Substance The mole defines the number of particles of a substance. It equals the amount of substance which contains 6.02 x particles (e.g. atoms or molecules). Luminous Intensity The unit of luminous intensity is the candela. Derived Units Derived units are those formed by combining basic units. The names and symbols of some of the units formed can be replaced by special names and symbols. The SI is not static but evolves to match the world's increasingly demanding requirements for measurement.

3 Prefixes A given SI unit may sometimes be too large or small for convenience. Thus standard fractions and multiples of the SI unit are used and are written by placing a prefix before the unit. Fraction Prefix Symbol 10-3 milli- m 10-6 micro- μ 10-9 nano- n pico- p Multiple Prefix Symbol 10 3 kilo- k 10 6 mega- M 10 9 giga- G tera- T Fraction or multiple Prefix Symbol 10 2 hecto- h 10 1 deca- dc 10-1 deci- d 10-2 centi c Scientific Notation When an expression is extremely large (mass of the earth) or indeed extremely small (mass of an electron) scientific notation is used. The basic format of scientific notation is M*10 n, where M is any real numbers between 1 and 10 and n is a whole number = = 10 x 10 x 10 = = 1/100 = = = 10 x 10 x 10 x 10 = 10, = 1/1000 = = 10 x 10 = = 1/10 = = 1/10000 = The earths mass is about 6,000,000,000,000,000,000,000,000 kg and written as 6.0 x kg. The electrons mass is kg and written as 9.11 x kg.

4 Significant Digits The significant digits represent the valid digits of a number. The following rules summarise the significant digits: Non-zero digits are always significant. All final zeros after the decimal points are significant. Zeros between two other significant digits are always significant. Zeros used solely for spacing the decimal point are not significant. Values #of significant digits In addition and subtraction, answers should be rounded up to the least precise measurement = = (3.21 is the least precise measurement) In multiplication and division, answers should be rounded up to the least number of significant digits: 3.22 x 2.1 = = 6.8 (2.1 contains 2 significant digits) In a problem with a mixture of addition, subtraction, multiplication or division, round your answer only at the end of the calculation. 3.6 x = = 3.12 = 3.2

5 Graphing data Graphs enable you to present data is a format that is easily understood. Data pairs - Graphs are made using pairs of numbers. Each pair of numbers represents on data point on the graph. The first number represents the independent variable and is plotted on the X-axis. The second number represents the dependent variable and is plotted in the Y-axis. Axis labels - Both axis should be labelled with the variable name and its units of measure. Data range - The data range on a graph can be calculated the subtracting the smallest value from the largest value. Title - All graphs should be titled in the format Dependent variable name v Independent variable name Mathematical Relationships The three most common types of mathematical relationships used in physics include: The Linear relationship This can be expressed by the equation y = mx +b, where m is the slope and b is the y intercept. The quadratic relationship This can be expressed by the equation y = kx 2, where k is a constant. The inverse relationship This can be expressed by the equation xy = k, where k is a constant.

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