Measurements and Units

Quantity and Unit Physical Quantities : are something that can be measured and expressed with certain value or number (quantified) and having a related unit

Basic quantities Base Quantities are physical quantities that have their own unit Physical Quantity S.I. Unit Symbol Length metre m Mass kilogram kg Temperature Kelvin K Time second S Luminous Intensity Candela Cd Electric Current Ampere A Amount of Molecul Mol mol

Derived Quantities Derved Quantities are quantities that come from basic quantities. The unit are more complex because it combine two or more basic quantities. Example: Area, volume, density, force, pressure, power, energy, etc.

Unit Conversion Unit conversion is changing a certain unit of aphysical quantity to other unit without changing its value. Prefix Value Symbol giga One billion G mega One milion M kilo One thousand k deci One tenth d centi One hundredth c milli One thousandth m micro One millionth μ nano One billionth n

2.1 Measurements in Daily Life We often make measurements in our daily lives, either accurately or by estimations. Measuring ingredients in recipes is one such example. It is important, however, to use standard units to take accurate measurements.

2.2 Units of Measurements Measurements are expressed in two parts – the numerical value and the unit. The numerical value tells us how much there is of something. The unit tells us the standard that we are comparing the value to. unit numerical value

2.3 Measuring Length Length is the distance between two specified points. Examples of measurements of length: height, depth, width, thickness and circumference S.I. unit of length is metre. The symbol for the metre is m.

Instruments for measuring length Metre rule To measure the length of an object using a metre rule, place one end of the object against the zero mark, and read off the mark on the rule at the other end of the object When your eye is in the wrong position for viewing the measurement, parallax error occurs. We can avoid parallax error by turning up the ruler instead of lying it flat.

Instruments for measuring length Measuring tape A measuring tape is used for measuring lengths greater than 1 m. A special property of the measuring tape is that it is soft and flexible, and are often used in measuring the diameters of round objects.

Instruments for measuring length Vernier calipers Vernier calipers are able to measure short lengths and diameters of objects of up to 10 cm. They are more accurate than the metre rule since the smallest division on the vernier scale is 0.01 cm compared to 0.1 cm on the metre rule. A pair of vernier calipers http://en.wikipedia.org/wiki/Image: Messschieber.jpg

Instruments for measuring length Using the vernier calipers Step 1: Close the jaws of the vernier calipers. Make sure that the zero marking on the vernier scale is in line with the zero marking on the main scale. Step 2: Place the object within the jaws of the vernier calipers and clamp it firmly in place. Step 3: Read the length.

Instruments for measuring length Using the vernier calipers

Instruments for measuring length Using the vernier calipers Zero error Positive zero error occurs when the jaws of the vernier calipers are closed and the zero marking on the vernier scale falls on the right of the zero marking on the main scale. Negative zero error occurs when the jaws of the vernier calipers are closed and the zero marking on the vernier scale falls on the left of the zero marking on the main scale.

Instruments for measuring length Choosing instruments Length to be measured Instrument to use Accuracy of instrument Between 0 and 10 cm Vernier calipers To the nearest 0.01 cm 10 cm – 100 cm Metre rule To the nearest mm 5 cm and above Measuring tape or contractor’s rule To the nearest mm (short lengths) To the nearest cm (very long lengths)

2.4 Measuring Area S.I. unit for area is square metre and represented by the symbol m2. Other common units for area are square millimetre (mm2), square centimetre (cm2) and square kilometre (km2).

2.4 Measuring Area Regular figures: use the right formula to calculate area h b a b a a Triangle Square Rectangle Area = ½ x b x h Area = a x a Area = b x a r h b Circle Parallelogram Area = πr 2 Area = b x h

2.4 Measuring Area Irregular figures Estimation of its area can be done with the help of a square grid whose sides are of known lengths. For example, if the sides are each 1 cm in length, the area of the square is 1 cm x 1 cm = 1 cm2

2.5 Measuring Volume The volume of an object is the amount of space it occupies. The S.I. unit for volume is cubic metre and represented by the symbol m3. Other common units for volume are the cubic centimetre (cm3), litre (l) and the millilitre (ml).

2.5 Measuring Volume Liquids The volumes of liquids can be measured using the measuring cylinder, burette or pipette.

2.5 Measuring Volume Liquids Reading the meniscus In narrow glass cylinders, the liquid level is curved into a shape called the meniscus (see diagram in the next slide). Position your eye at the same level as the bottom of the meniscus to get the correct reading and avoid parallax error.

2.5 Measuring Volume Liquids Reading the meniscus meniscus

2.5 Measuring Volume Regular solids: use the right formula to calculate volume l b h l h r l l Cube Cuboid Cylinder Volume = l x l x l Volume = l x b x h Volume = πr 2h h r r Sphere Cone Volume = 4/3 πr 3 Volume = 1/3 πr 2h

2.5 Measuring Volume Irregular solids The volume of a small, irregular solid can be measured by displacement. This can be done with the aid of a measuring cylinder or a displacement can.

2.6 What is mass? Mass is a measure of the amount of matter in a body. S.I. unit of mass is kilogram, and represented by the symbol kg. Other common units for mass are grams (g), milligrams (mg), and tonnes (t).

Measuring mass Balances are used to measure mass. A beam balance uses known masses to measure the mass of an unknown object. An electronic balance measures the mass of an object when the object is placed on the metal pan and the reading is displayed. Beam balance Electronic balance

Measuring time So many tools that we use to measuring time Sun clock Stop watch Atomic clock Wall clock

Miscellaneous http://physics.nist.gov/cuu/Units/ http://www.unc.edu/~rowlett/units/ http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=52 http://www-istp.gsfc.nasa.gov/stargaze/Smass.htm http://en.wikipedia.org/wiki/Mass http://en.wikipedia.org/wiki/Density