Units, Measurements & Instruments: Foundations for Physics

Units, Measurements & Instruments

Learning Outcomes

By the end of this section, students should be able to:

• Define SI base units and derived quantities.

• Use measuring instruments correctly (ruler, caliper, balance, multimeter).

• Convert between units using dimensional analysis.

• Recognize the importance of precision and accuracy in measurements.

SI Base Units and Derived Units

Definition and Importance

The International System of Units (SI) provides a standardized set of units for scientific measurement, ensuring consistency and clarity in communication and calculation.

• Base Units: The seven fundamental quantities in SI are:

  • Length: meter (m)

  • Mass: kilogram (kg)

  • Time: second (s)

  • Electric current: ampere (A)

  • Temperature: kelvin (K)

  • Amount of substance: mole (mol)

  • Luminous intensity: candela (cd)

• Derived Units: Formed by combining base units according to physical relationships.

  • Speed: meter per second (m/s)

  • Force: newton (N), where $1\,\text{N} = 1\,\text{kg} \cdot \text{m}/\text{s}^2$

  • Pressure: pascal (Pa), where $1\,\text{Pa} = 1\,\text{N}/\text{m}^2$

  • Energy: joule (J), where $1\,\text{J} = 1\,\text{N} \cdot \text{m}$

SI Prefixes

SI prefixes indicate multiples or submultiples of units, making it easier to express very large or small quantities.

Prefix	Symbol	Factor
kilo	k	$10^3$
centi	c	$10^{-2}$
milli	m	$10^{-3}$
micro	\mu	$10^{-6}$
nano	n	$10^{-9}$
mega	M	$10^6$
giga	G	$10^9$

Measuring Instruments

Common Tools and Their Uses

Accurate measurement is essential in physics. The following instruments are commonly used:

• Ruler & Vernier Caliper: Measure length and small distances with varying precision.

• Balance: Measures mass.

• Stopwatch: Measures time intervals.

• Multimeter: Measures voltage, current, and resistance in electrical circuits.

Example: A Vernier caliper can measure the diameter of a small cylinder more precisely than a standard ruler.

Unit Conversion & Dimensional Analysis

Unit Conversion

Unit conversion is the process of changing a quantity from one unit to another using conversion factors.

• Example: Convert 72 km/h to m/s:

$72\,\text{km/h} = 72 \times \frac{1000\,\text{m}}{1\,\text{km}} \times \frac{1\,\text{h}}{3600\,\text{s}} = 20\,\text{m/s}$

Dimensional Analysis

Dimensional analysis is a method for checking the correctness of equations by comparing the dimensions on both sides.

• Dimensions represent the physical nature of a quantity (e.g., mass [M], length [L], time [T]).

• Example: Velocity has dimensions of length divided by time: $[L][T]^{-1}$.

Unit Conversion Examples

• Speed: A tuk-tuk is travelling at 60 km/h. Convert to m/s:

  • $60\,\text{km/h} = 60 \times \frac{1000}{3600} = 16.67\,\text{m/s}$

• Pressure: Atmospheric pressure at sea level is 1 atm. Convert to Pa and N/cm2:

  • $1\,\text{atm} = 1.013 \times 10^5\,\text{Pa}$

  • $1\,\text{Pa} = 1\,\text{N}/\text{m}^2$

• Energy: Electricity bill shows energy use of 1 kWh. Convert to Joules:

  • $1\,\text{kWh} = 1000\,\text{W} \times 3600\,\text{s} = 3.6 \times 10^6\,\text{J}$

• Land Area: A land plot is 20 perches. Convert to m2:

  • $1\,\text{perch} = 25.29\,\text{m}^2$ so $20\,\text{perches} = 505.8\,\text{m}^2$

What is Dimensional Analysis?

Purpose and Method

• Checks the correctness of equations using fundamental dimensions.

• Base quantities: Mass (M), Length (L), Time (T), Current (I), Temperature (Θ).

• Example: For velocity, $\text{velocity} = \frac{\text{distance}}{\text{time}} \rightarrow [L][T]^{-1}$

Application: If both sides of an equation do not have the same dimensions, the equation is not physically meaningful.

Additional info: Precision refers to the consistency of repeated measurements, while accuracy describes how close a measurement is to the true value. Both are crucial for reliable scientific results.