Units and Measurement

• Measurement is comparing an unknown quantity to a known, accepted standard.
• Early units of measurement were based on body parts, but were unreliable due to lack of standardization.
• In the 1790s, the metric system (CGS) was developed in Paris.
• The metric system evolved into the Système International d'Unités (SI units) in 1960.

Standard Units

• Volume is measured in litres.
• Weight is measured in grams.
• Length is measured in metres.
• Scientific progress relies on precise measurement of particles.

Direct vs. Indirect Measurement

• Direct measurements are taken directly from calibrated instruments.
• Indirect measurements are calculated using formulas.
• Vernier callipers and micrometers provide more accurate length measurements than rulers or tape measures.
• A furlong equaled the length an ox team could plough without rest.
• An acre equaled the area an ox team could plough in a day.

Seven Basic Units of Measurement

• Metre (m) measures length.
• Kilogram (kg) measures mass.
• Second (s) measures time.
• Kelvin (K) measures temperature.
• Ampere (A) measures electric current.
• Mole (mol) measures the amount of substance.
• Candela (cd) measures luminous intensity.
• These units are fundamental because they cannot be derived from each other

Importance of Standard Measurement

• Universal standardization of units is necessary for trade and accurate measurements in science and technology.
• Measurements are vital for monitoring pollution levels.
• Accurate measurements are needed to ensure safe drinking water.
• Standard dimensions are needed so products fit together.

Key Terms

• Physical quantities are measurable in physics
• Fundamental physical quantities cannot be defined by other quantities
• Derived physical quantities can be defined by fundamental physical quantities
• A unit is the smallest quantity used to measure other quantities

Fundamental and Derived Units

• Fundamental units cannot be derived from any other unit (e.g., length, mass, time).
• Derived units are combinations of fundamental units (e.g., area, volume, density).

Measurement Essentials

• A measure is a reference standard for comparing physical quantities.
• Measurement consists of a number, and a unit.
• A measurement without a unit is meaningless.
• Standard units are necessary for universal understanding.
• The International System of Units is the official name of the metric system.
• There are seven basic units in the metric system based on fundamental quantities.

Fundamental Quantities and SI Units

• Length is measured in metres (m).
• Mass is measured in kilograms (kg).
• Time is measured in seconds (s).
• Electric current is measured in amperes (A).
• Thermodynamic temperature is measured in kelvin (K).
• Amount of substance is measured in moles (mol).
• Luminous intensity is measured in candelas (cd).
• Plane angle is measured in radians (rad)

Measurement Systems

• CGS system (centimetre-gram-second) measures small masses, lengths, and times.
• MKS system (metre-kilogram-second) measures large masses, lengths and times
• SI system (Système International) Includes all fundamental units.
• FPS system (foot-pound-second) is part of the British system

Derived Units

• Derived units are obtained by combining fundamental units.
• Area is measured in square units (Length x Length).
• Volume is measured in cubic units (Length x Length x Length).
• Velocity is measured in terms of length and time.

Derived SI Units

• Area is measured in square metres (m²).
• Volume is measured in cubic metres (m³).
• Velocity is measured in metres per second (m/s).
• Acceleration is measured in metres per second squared (m/s²).
• Force is measured in newtons (N) or kg⋅m/s².
• Work and energy are measured in joules (J) or kg⋅m²/s².
• Power is measured in watts (W) or kg⋅m²/s³.
• Momentum is measured in kilogram metres per second (kg⋅m/s).

SI Units and What They Measure

• Newton (N) measures force.
• Joule (J) measures work and energy.
• Watt (W) measures power.
• Coulomb (C) measures electrical charge.
• Hertz (Hz) measures frequency.
• Pascal (Pa) measures pressure and stress.
• Volt (V) measures voltage.
• Ohm (Ω) measures electrical resistance.

Metre and Kilogram

• A metre is the distance light travels in a vacuum in 1/299,792,458 of a second.
• The kilogram is the mass of a platinum-iridium alloy standard.

Least Count of an Instrument

• The least count is the smallest, accurate value that can be resolved on an instrument's scale.
• An instrument with a smaller least count is more accurate
• Measurement is repeatable to the resolution of the least count.
• Least count is inversely proportional to the accuracy of the instrument.

Examples of Least Count

• A sundial (hours) has a larger least count as compared to a stopwatch (tenths of a second)
• Ordinary wall clock has a least count of 60 seconds (1 minute).
• The least count is determined by dividing the smallest main scale reading by the total number of divisions on the secondary scale.
• The smallest value that can be measured by the measuring instrument

Examples of Instruments and Least Count

• Metre scale: 0.1 cm (1 mm)
• Vernier calliper: 0.01 cm (0.1 mm)
• Micrometer screw gauge: 0.001 cm (0.01 mm)
• Analog stopwatch: 0.1 second
• Digital stopwatch: 0.01 second
• Physical balance: 0.1 kg (100 g)
• Digital weighing scale: 0.01 g

Measuring Length

• Common length-measuring tools include yardsticks, metre sticks, steel rules, measuring tapes, micrometers, vernier callipers, and screw gauges.
• Accuracy varies from 1/32" with a yardstick to 0.001" with a micrometer screw gauge.

Linear Measures

• Measurement of length is called linear measure.
• The British system is widely used in the US.
• The inch is the smallest unit in the British Imperial System.
• Fractional divisions of an inch include halves, quarters, eights, and sixteenths.
• Steel rules are more accurate than yardsticks or steel tapes.

Units of Length

• Three convenient units to measure length are the metre, angstrom (Å), and light year.
• 1 Å = 10⁻¹⁰ m.
• 1 light year = 9.461 x 10¹⁵ m.

Using a Ruler (Metre Scale)

• Align the 0 mark with one end of the object to avoid errors.
• Subtract the reading at one end from the reading at the other end.
• Keep your eye vertically above the reading to avoid parallax error.

Parallax Error and Limitations

• Parallax error occurs when viewing the scale at an angle.
• A metre scale can measure length to 1 mm (0.1 cm), which is the least count of the metre scale.
• Vernier callipers are used for measurements up to 0.1 mm (0.01 cm).

Vernier Calliper

• Used to measure internal and external diameters, depths of vessels, and wire thickness.
• It consists of a main scale and a sliding vernier scale.
• Jaws measure external dimensions
• Sliding strip measures the depth of hollow objects.

Vernier Scale

• A sliding jaw carries an auxiliary scale known as the vernier scale.
• Each division on the vernier scale is slightly shorter than a division on the main scale.
• Vernier scales provide measurements accurate to the second decimal place.

Working of Vernier Calliper

• Determine the least count (LC)
• Determine the zero error if any

Determining Least Count

• If 'm' is the number of divisions in one centimetre of the main scale, the least count of the main scale is 0.1 cm.
• If 'n' is the number of divisions on the vernier scale, 'n' vernier scale divisions occupy the same length as (n-1) divisions of the main scale.
• LC of vernier calliper = Least count of main scale / Number of divisions on vernier scale.
• Usually, n = 10, then the LC of the vernier calliper = 0.1 cm / 10 = 0.01 cm.

Zero Error

• Zero error is the distance between the zero of the main scale and the zero of the vernier scale when the jaws are closed.
• Zero error can be positive or negative
• Subtract the zero error (with the correct sign) from the observed reading.

Positive Zero Error

• The zero mark of the vernier scale is to the right of the zero mark of the main scale.
• Multiply the vernier division that coincides with a main scale division by the least count to find the zero error.

Negative Zero Error

• The zero mark of the vernier scale is to the left of the zero mark of the main scale.
• Subtract the coinciding vernier division number from the total number of vernier scale divisions, then, multiply the difference by the least count.