Measurement and Units Skills for Physics

SI Units Over the centuries many different units for measuring physical quantities have been developed. For example... Lengths can be measured in chains, fathoms, furlongs, yards, feet, rods and microns.

SI Units The metric system was established by the French Academy of Science at the time of the French Revolution (1789–1815). This system includes units such as the metre, litre and kilogram. Countries of the British Empire adopted the British Imperial system of the mile, gallon and pound.

SI Units Having separate systems made it harder for scientists to communicate and compare data. It also made it harder for merchants to trade goods. In 1960 an international comittee set standard units for fundamental physical quantities. These were called the Système Internationale d’Unites (in French). We know them as the SI units.

* Base Units At this point ask students to write down why they think we need to have a standard set of units.

Mass The kilogram was originally defined as the mass of 1 L of water at 4°C. Since 1897 the measurement standard for the kilogram has been a cylindrical block of platinum– iridium alloy kept at the International Bureau of Weights and Measures in France. Australia has a copy of this at the CSIRO Division of Applied Physics in Sydney. At times it is returned to France to ensure that the mass remains accurate.

Length The metre was originally defined in 1792 as one ten- millionth of the distance from the equator to the North Pole. In 1983, to give a more accurate value, the metre was redefined as the distance that light in a vacuum travels in 1/299 792 458 second. This can be reproduced all over the world, as light travels at a constant speed in a vacuum.

Time Until 1960, one second was defined as 1/60 of 1/60 of 1/24 of an average day in 1900. Unfortunately the Earth’s rotation on its axis not quite uniform. In 1967 one second was defined as the time required for a caesium-133 atom to undergo 9 162 631 770 vibrations.

Derived Units Derived units are defined in terms of the base SI units. For example... Velocity has unit m s-1 Force has unit kg m s-2

* Derived Units Ask students to think of some other derived units.

Negative Indices Derived units are often expressed with negative indices. For example, the unit of speed is usually expressed as m s−1 rather than m/s because... The unit of pressure, newtons per square metre, or N/m2, is written as N m−2 because...

Prefixes Some SI units are too large or small for measuring some quantities. For example, consider measuring... the thickness of a human hair in metres the age of the Earth in seconds The prefixes used in front of SI units allow you to use more appropriate units such as millimetres or kilometres

* Prefixes Ask students to think of some other measurements that would be inappropriate with the SI units.

Correct use of symbols Uppercase letters are not used for the names of quantities (eg: newton). Uppercase letters are only used for symbols that are named after people (eg: N). The one exception to this is the litre (L).

Correct use of symbols * For a derived unit which is the product of two other units the unit symbols are separated by a dot or a space (eg: N m or N.m) Units involving the division of other units can be shown as a fraction or a negative index (eg: m/s or ms-1) Prefixes should not be separated by a space. What is wrong with these: ms-2, k m/h, µM, Nm

Practice questions For these questions you will need to refer to... the table of SI units on page 563 the table of derived units on page 564 the table of prefixes on page 566 Write the full name for the following units a. dm b. mA c. nJ d. µg Express each of the following quantities in SI base units a. 1500 mA b. 250 GW (note 1W = 1 J s-1) c. 150 µs d. 12 dm What is the SI unit for acceleration if

Accuracy and Precision Often the terms accuracy and precision are used interchangeably, however they are not the same thing and the difference between them is important in Physics. Accurate measurements are, on average, a good representation of the actual value. Precise measurements have very little variation between consecutive readings.

Accuracy and Precision

Accuracy and Precision * Accuracy and Precision The precision of a instrument determines the uncertainty in a measurement. The uncertainty (sometimes called error) is generally one half of the finest scale division on the measuring instrument. Examples... What is the uncertainty in each of these? Perhaps don’t ask students to write these down as they can’t write the question.

Significant figures When we take a measurement the number of significant figures we write down reflects the uncertainty of the measuring device. Examples... 5.5 m 16.5 cm 16.25 cm What is the uncertainty in each of these? Perhaps don’t ask students to write these down as they can’t write the question.

Significant figures Significant figures and decimal places are two different things. To determine the number of significant figures in a value follow these rules... Zeros between other numbers are significant eg: 1001 Zeros before other numbers are not significant eg: 0.01 For zeros after other numbers... To the right of the decimal point they are significant eg: 0.10 To the left of the decimal point they are significant unless stated otherwise eg: 8000

Significant figures Practice questions Round the following to... i) 1 decimal place ii) 2 decimal places a) 7.953 b) 12.076 c) 0.083 d) 100.999 e) 33.333 f) 6.12059 Round each of the following numbers to the number of significant figures shown in the brackets. a) 4.397 (1) b) 758.92 (1) c) 1200.56 (2) d) 3.5009 (3) e) 0.0762 (2) f) 19.0583 (4) How many significant figures are there in the following... a) 100.029 b) 9.250 c) 0.029

Significant figures Round the following to the number of decimal places shown in the brackets. a) 9.259 (2) b) 12.076(1) c) 0.083(0) Round each of the following numbers to the number of significant figures shown in the brackets. a) 2700.397 (1) b) 257.83 (3) c) 2.15007 (2) Evaluate the following to the correct numbers of significant figures. a) The area of a circle with a radius of 10.0 cm b) The volume of milk left in a 1 L carton after 300 ml has been removed.

Scientific notation To make it clear how many significant figures there are in a value scientists use scientific notation. In scientific notation values are written as a number between 0 and 10, then multiplied by a power of 10. Example: 0.054 = 5.4 × 10-2 245.7 = 2.457 × 102 Note that scientific notation, standard notation and standard form all have the same meaning.

Scientific notation Practice questions Express the following quantities in scientific notation: (a) the radius of the Earth, 637 000 m (b) the speed of light in a vacuum, 300 000 000 m s−1 (c) the diameter of a typical atom, 0.000 000 000 3 m The speed of light in a vacuum is 2.9979 × 108 ms-1 , write this without using scientific notation.