Measurements In Physics

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SI Base Units

All physical quantities can be reduced to seven base units known as the SI Base Units.
The seven SI base quantities and their units are: mass (kilogram, kg), length (metre, m), time (second, s), current (ampere, A), temperature (kelvin, K), amount of substance (mole, mol), and luminous intensity (candela, cd).
The candela is the seventh base unit, measuring luminous intensity, but it is not covered in IB Physics.
The SI system is officially used in almost every country around the world.

Derived Units

Derived units are formed from combinations of the seven SI base units.
To deduce the base units of a derived quantity, use the defining equation for that quantity.
The newton (N), the unit of force, is defined by Force = mass × acceleration, so N = kg m s⁻².
The joule (J), the unit of energy, is defined by Energy = ½ × mass × velocity², so J = kg m² s⁻².
The pascal (Pa), the unit of pressure, is defined by Pressure = force ÷ area, so Pa = kg m⁻¹ s⁻².

Scientific Notation and Orders of Magnitude

Scientific notation expresses numbers as a digit before the decimal point multiplied by a power of 10, e.g., 4.6 × 10⁶.
The order of magnitude of a number is the nearest power of 10; if the digit is 5 or more, round up to the next power of 10.
A quantity is an order of magnitude larger than another if it is about ten times larger; two orders of magnitude means 100 times larger.
Orders of magnitude help compare very large or very small quantities, such as the diameter of the Milky Way (≈10²¹ m) or the length of a bacteria cell (≈10⁻⁶ m).
Estimation involves obtaining approximate values, often to the nearest order of magnitude.

Metric Multipliers

Metric multipliers are prefixes that change the size of a unit by powers of 10.
Common prefixes include: peta (P, 10¹⁵), tera (T, 10¹²), giga (G, 10⁹), mega (M, 10⁶), kilo (k, 10³), centi (c, 10⁻²), milli (m, 10⁻³), micro (μ, 10⁻⁶), nano (n, 10⁻⁹), pico (p, 10⁻¹²), femto (f, 10⁻¹⁵).
Prefixes are represented by single-letter symbols placed before the unit, e.g., cm for centimetres or GW for gigawatts.
You are expected to know common metric multipliers for exams.

Significant Figures

Significant figures are the digits that accurately represent a quantity and indicate its precision.
Rule 1: In an integer, all digits count as significant if the last digit is non-zero (e.g., 702 has 3 s.f.).
Rule 2: Zeros at the end of an integer do not count as significant (e.g., 705,000 has 3 s.f.).
Rule 3: Zeros in front of an integer do not count as significant (e.g., 0.002309 has 4 s.f.).
Rule 4: Zeros at the end of a number less than zero count as significant, but those in front do not (e.g., 0.0020300 has 5 s.f.).
Rule 5: Zeros after a decimal point are significant (e.g., 70.0 has 3 s.f.).
When combining numbers, the result should be given to the smallest number of significant figures in the calculation.

Dimensional Analysis

Dimensional analysis checks the homogeneity of physical equations using SI base units.
The units on both sides of an equation must be the same.
To check homogeneity, compare the units on each side; if they do not match, the equation is incorrect.

Measurement Techniques and Instruments

Common instruments include: metre rules (length), thermometers (temperature), measuring cylinders (volume), balances (mass), Newtonmeters (force), protractors (angles), stopwatches (time), ammeters (current), voltmeters (potential difference), sound meters (sound intensity), and light meters (light intensity).
More precise instruments like the micrometer screw gauge and Vernier calipers measure thicknesses, diameters, and lengths to a greater accuracy.
The resolution of an instrument is the smallest change in a quantity that produces a change in reading.
A higher resolution means smaller changes can be detected; for example, a digital thermometer (0.1°C) has higher resolution than a mercury thermometer (1°C).
Typical resolutions: metre rule 1 mm, Vernier calipers 0.01 mm, micrometer 0.001 mm, top-pan balance 0.01 g, protractor 1°, stopwatch 0.01 s, thermometer 1°C, voltmeter 1 mV–0.1 V, ammeter 1 mA–0.1 A.

Controlling Variables and Calibration

For a valid experiment, all variables that may affect the outcome must be controlled.
The independent variable is the only variable changed; the dependent variable is measured; controlled variables are kept constant.
A fair test is one in which only the independent variable affects the dependent variable.
Calibration compares a known measurement with the instrument's reading to check accuracy and avoid zero error.
Calibration curves convert measurements from one scale to another, useful when instrument output is not proportional to the measured value (e.g., thermocouple e.m.f. vs temperature).

Reducing Unwanted Energy Transfers

Heat loss/gain by conduction can be reduced using insulators with low thermal conductivity.
The effectiveness of an insulator depends on its thermal conductivity (lower is better), density (lower is better), and thickness (thicker is better).
Friction in mechanical systems causes unwanted heating; it can be reduced by adding bearings and lubricating parts.
Electrical resistance causes unwanted heating; it can be reduced by using lower-resistance components and reducing current.

Background Radiation

Background radiation comes from natural and artificial sources and varies with location.
When measuring radiation from a source, measure the background count first with a Geiger-Muller tube away from sources.
Subtract the background count from each reading to obtain the count rate from the source only.
To verify the inverse square law for gamma radiation, plot 1/√C against distance x; a straight line through the origin confirms the relationship.

Slides

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Practice questions

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1.Which of the following is NOT one of the seven SI base units?
Easy
- ANewton
- BKilogram
- CAmpere
- DKelvin
2.The unit of force, the newton (N), expressed in SI base units is:
Easy
- Akg m s⁻²
- Bkg m² s⁻²
- Ckg m s⁻¹
- Dkg m² s⁻³
3.Which of the following are SI base quantities? (select all that apply)
Medium
- AMass
- BForce
- CTime
- DEnergy
- ETemperature
4.The order of magnitude of 6 × 10⁸ is 10⁹.
Easy
True or false?
5.Match each physical quantity with its SI base unit.
Medium
- Mass
- Length
- Time
- Current
- Temperature
- Kilogram
- Metre
- Second
- Ampere
- Kelvin
6.Arrange the following metric multipliers in order from smallest to largest.
Medium
- milli
- centi
- deci
- deca
- kilo
7.The order of magnitude of 3 × 10⁸ is 10⁸.
Easy
True or false?
8.A student measures the background radiation count in a laboratory and obtains the following readings: 12, 14, 13, 11, 15 counts per minute. What is the mean background count rate?
Medium
- A13 counts/min
- B12 counts/min
- C14 counts/min
- D15 counts/min

Flashcards

What are the seven SI base units?

The seven SI base units are: kilogram (kg) for mass, metre (m) for length, second (s) for time, ampere (A) for current, kelvin (K) for temperature, mole (mol) for amount of substance, and candela (cd) for luminous intensity.

What is a derived unit?

A derived unit is a unit that is derived from the seven SI base units, such as newtons (N), joules (J), and pascals (Pa).

Express the newton (N) in SI base units.

The newton (N) is defined as kg m s⁻².

Express the joule (J) in SI base units.

The joule (J) is defined as kg m² s⁻².

Express the pascal (Pa) in SI base units.

The pascal (Pa) is defined as kg m⁻¹ s⁻².

What is an order of magnitude?

An order of magnitude is the power of 10 when a number is expressed in scientific notation. For example, the order of magnitude of 3 × 10⁸ is 10⁸.

How do you determine the order of magnitude of a number?

If the number is greater than 5, round up to the next power of 10; if less than 5, keep the same power of 10. For example, 6 × 10⁸ has order of magnitude 10⁹.

What is scientific notation?

Scientific notation is a way of writing numbers as a product of a number between 1 and 10 and a power of 10, e.g., 4.6 × 10⁶.

What are metric multipliers?

Metric multipliers are prefixes used with SI units to indicate multiplication by a power of 10, such as kilo- (k) for 10³, centi- (c) for 10⁻², and milli- (m) for 10⁻³.

List the common metric multipliers and their values.

peta (P) 10¹⁵, tera (T) 10¹², giga (G) 10⁹, mega (M) 10⁶, kilo (k) 10³, hecto (h) 10², deca (da) 10¹, deci (d) 10⁻¹, centi (c) 10⁻², milli (m) 10⁻³, micro (μ) 10⁻⁶, nano (n) 10⁻⁹, pico (p) 10⁻¹², femto (f) 10⁻¹⁵.

What are significant figures?

Significant figures are the digits in a number that carry meaning contributing to its precision. They indicate the accuracy of a measurement.

State the rules for determining significant figures.

1. All non-zero digits are significant. 2. Zeros between non-zero digits are significant. 3. Leading zeros are not significant. 4. Trailing zeros in a number with a decimal point are significant. 5. In an integer without a decimal point, trailing zeros may or may not be significant (usually not).

How many significant figures are in 0.0020300?

5 significant figures.

What is dimensional analysis?

Dimensional analysis is a method to check the homogeneity of physical equations by comparing the SI base units on both sides of the equation.

What is the principle of homogeneity in dimensional analysis?

The principle states that the units on both sides of a physical equation must be the same.

Name common instruments used to measure length, mass, time, and temperature.

Length: metre rule, Vernier calipers, micrometer. Mass: balance. Time: stopwatch. Temperature: thermometer.

What is the resolution of a measuring instrument?

The resolution is the smallest change in a physical quantity that causes a detectable change in the reading of the instrument.

What is the typical resolution of a metre rule, Vernier calipers, and micrometer?

Metre rule: 1 mm; Vernier calipers: 0.01 mm; micrometer: 0.001 mm.

Why is calibration of measuring apparatus important?

Calibration checks the accuracy of an instrument by comparing its readings to a known standard, helping to avoid zero errors and ensure reliable measurements.

What is a fair test in an experiment?

A fair test is one in which only the independent variable affects the dependent variable; all other variables are controlled.

How can heat loss by conduction be reduced?

Use materials with low thermal conductivity (insulators), increase thickness, and reduce density of the insulating material.

How can friction be reduced in mechanical systems?

By adding bearings, lubricating parts, and using smoother surfaces.

How can electrical resistance be reduced in circuits?

By using components with lower resistance and reducing the current.

How is background radiation accounted for in experiments?

Measure the background count without the source, then subtract this from each reading with the source to obtain the corrected count rate.

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