Study sheet: Physics and Measurement

📋 Course Outline

1. Physical Quantities and Units
2. SI Base and Derived Units
3. Prefixes and Unit Conversion
4. Measurement Accuracy and Precision
5. Measurement Uncertainty

📖 1. Physical Quantities and Units

🔑 Key Concepts & Definitions

• Physical quantity : a measurable property used to describe physical phenomena and is specified by a numerical value and a unit.

★ Must-know

📐 Formula — A length of $l=2.5\,m$ has the quantity symbol $l$, the numerical value $2.5$, and the measurement unit $m$.

Further detail

📌 A numerical value states the magnitude of a measurement, whereas a unit identifies the standard used to measure it.

💡 Memory Hook

A number alone is incomplete; a physical quantity needs number + unit.

📖 2. SI Base and Derived Units

🔑 Key Concepts & Definitions

• SI system : a system established to standardize measurements.

📝 Essential Points

• The seven SI base quantities are:

  • length
  • mass
  • time
  • electric current
  • thermodynamic temperature
  • amount of substance
  • luminous intensity

• The SI units and symbols are:

  • metre (m) for length
  • kilogram (kg) for mass
  • second (s) for time
  • ampere (A) for electric current
  • kelvin (K) for thermodynamic temperature
  • mole (mol) for amount of substance
  • candela (cd) for luminous intensity

📌 A derived quantity is constructed from base quantities; for example, speed satisfies $v=\frac{\Delta x}{\Delta t}$ and has the unit $m/s$.

💡 Memory Hook

L-M-T-I-Θ-N-J: the seven SI base quantities.

📖 3. Prefixes and Unit Conversion

🔑 Key Concepts & Definitions

• Measurement prefix : expresses very large or very small quantities as powers of ten relative to a base unit.

★ Must-know

• The important prefixes are kilo for $10^3$, hecto for $10^2$, deci for $10^{-1}$, centi for $10^{-2}$, milli for $10^{-3}$, micro for $10^{-6}$, and nano for $10^{-9}$.

• Converting $3.5\,cm$ to metres gives $3.5\,cm=3.5\times10^{-2}m$.

• Converting $72\,km/h$ to SI speed units gives $72\,km/h=20\,m/s$ by multiplying by $\frac{1000m}{1km}\times\frac{1h}{3600s}$.

Further detail

📐 Formula — The conversions are $1\,km=10^3m$, $1\,cm=10^{-2}m$, and $1\,mm=10^{-3}m$.

💡 Memory Hook

kilo → hecto → deci → centi → milli → micro → nano.

📖 4. Measurement Accuracy and Precision

🔑 Key Concepts & Definitions

• Accuracy : indicates how close a measurement is to the true value.
• Precision : indicates how close the results of several measurements are to one another.

★ Must-know

• No measurement is completely free of error.

Further detail

• A measurement depends on the accuracy of the instrument, the measurement method, and the experimental conditions.

• Several measurements can be very close to one another while all remaining far from the true value.

💡 Memory Hook

Accuracy means closeness to the true value, whereas precision means closeness among repeated results.

📖 5. Measurement Uncertainty

🔑 Key Concepts & Definitions

• Measurement uncertainty : the estimated range associated with a measured value because the true value cannot be known exactly.

📝 Essential Points

📐 Formula — Reporting $L=(12.4\pm0.1)\,cm$ means that the measured length is approximately $12.4\,cm$ with an uncertainty of $0.1\,cm$.

• The true value is expected to lie within a range around the measured value.

• 🔄 When solving a physics problem,: identify the quantity, identify its unit, check whether the units are consistent, convert units if necessary, report the result with an appropriate number of digits

💡 Memory Hook

Measurement limitations → uncertainty → an interval around the measured value.

📊 Synthesis Tables

Accuracy and Precision

Concept	What it measures	Possible result
Accuracy	Closeness to the true value	A result can be accurate
Precision	Closeness among repeated results	Results can be precise but far from the true value