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PHY430 – Lecture 1

Physical Quantities & UnitsBase & Derived Quantities & SI Units

Dimensional AnalysisUnit Conversion

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Base quantity & Derived quantity Base quantity A quantity which is

not a combination of other physical quantities.

Must be defined in terms of a standard.

Units for base quantities are base units

Derived quantity A quantity which is

a combination of two or more physical quantities.

Units for derived quantities are derived units

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1 meter The meter is the

length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.

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1 kilogram A particular platinum-

iridium cylinder kept at the International Bureau of Weights and Measures near Paris.

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1 second One second is

defined as the time required for 9,192,631,770 periods of radiation emitted by cesium atoms.

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Effective technique of Unit Conversion

1. Write the unit in traditional form and not the index form.

eg.

2. Remember or look up the conversion factor.3. Multiply the initial quantity with the proper

conversion factor so that only the required units are left, the others cancelled off.

1msnotandsm

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Conversion factor to remember 1 km = 1000 m 1 m = 100 cm 1 cm= 10 mm 1 kg = 1000 g 1 h = 60 min 1 min = 60 s 1 h = 3600 s Remember the values for the prefixes. The rest – look up the conversion table

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Unit Conversion Convert (a) 110 km/h to m/s (b) 340 m/s to km/h (c) 300 m2 to cm2

(d) 20 m3 to cm3

(e) 1000 kg/m3 to g/cm3

(f) 15 nm to m (g) 25 A to A (h) 240 MW to kW

Dimensional Analysis

Dimensions of a quantity are base quantities or base units that make up the quantity

Dimensional Analysis is a useful technique to check if a relationship is incorrect

Add & subtract quantities only if they have the same dimensions

[LHS] = [RHS]

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Symbol for Dimension

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Quantity Symbol for DimensionLength L

Mass M

Time T

Volume

Velocity L/T

Density

Acceleration

3L

Eg. 1 Dimensional Analysis

Show that v = u + at is dimensionally correct.

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Significant Figures (sf)Rule

1. All non zero digits in a number are sf

2. Zero in between two non zero digits are sf

3. For any whole number, zero at the end of a number can be a sf or not a sf. It depends on the of precision of the reading.

Examples

1. (i) 3421 : 4 sf(ii) 62.5 : 3 sf

2. (i) 503 : 3 sf(ii) 1.006 : 4 sf

3. (i) 63 000 : 2 sf if the precision is to the nearest thousand(ii) 63 000 : 3 sf if the precision is to the nearest hundred

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Significant Figures (sf)Rule

4. For a decimal number less than 1, zero placed before any non-zero digit is not a sf.

5. For a decimal number, zero placed after a non-zero digit is a sf.

Examples

4. (i) 0.0028 : 2 sf(ii) 0.0902 : 3 sf

5. (i) 7.40 : 3 sf(ii) 0.020 : 2 sf

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Significant Figures : multiplication & division

The final results of multiplication or division should have only as many digits as the number with the least number of significant figures used in the calculation.

Eg. 11.3 x 6.8 = 76.84 = 77 (round off to 2 sf)

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