Fundamentals of Measurement and SI Units

Measurement: Observations and Tools

• Physicists begin with perception: make observations and ask fundamental questions such as:
  • How big is an object?
  • How much mass does it have?
  • How far did it travel?
• Measurements are made with various instruments (examples given): meter stick, balance, stopwatch, etc.

The Role of Units in Measurement

• Measurements of physical quantities are expressed in terms of units, which are standardized values.
• Example: a length measurement can be expressed in meters (m) for sprint distances or kilometers (km) for long distances.
• Without standardized units, it would be extremely difficult to express and compare measured values meaningfully.

System of Measurement: SI Base Principle

• All physical quantities in the International System of Units (SI) are expressed as combinations of seven fundamental physical units.
• The seven fundamental quantities are:
  • Length
  • Mass
  • Time
  • Electric current
  • Temperature
  • Amount of substance
  • Luminous intensity
• A measurement consists of a number and a unit.
• Physical Quantities are expressed as a combination of these base units; this is the foundation of dimensional analysis.

SI Base Units (Table 1)

• Length (Quantity): Meter; Symbol: m
• Mass: Kilogram; Symbol: kg
• Time: Second; Symbol: s
• Electric current: Ampere; Symbol: A
• Temperature: Kelvin; Symbol: K
• Amount of substance: Mole; Symbol: mol
• Luminous intensity: Candela; Symbol: cd

SI Units: Fundamental vs Derived

• Two main systems of measurement:
  • SI Units (Le Système International d’Unités), also known as the metric system
  • English Units (Imperial system)
• SI Units are logical, base-10, and easy to convert; this is a key advantage in science.
• The United States is one of the few countries that still widely uses English units.

Fundamental vs Derived Units

• Fundamental Units: seven base quantities are not made from any other units; they form the building blocks for all other units.
• Derived Units: created by combining fundamental units using multiplication and/or division.
• Examples of Derived Units:
  • Force: Newton (N)
  • Speed: meters per second (m/s)
  • Volume: cubic meters (m^3)
• Expressions and relations to base units often reveal the dimensional structure of physical laws.

What Are Units?

• In this course, we’ll mostly use five base quantities:
  • Length
  • Mass
  • Time
  • Electric current
  • Temperature
• Associated base SI units for these are:
  • Length → meter (m)
  • Mass → kilogram (kg)
  • Time → second (s)
  • Electric current → ampere (A)
  • Temperature → kelvin (K)
• Note: The seven base quantities also include Amount of substance (mole) and Luminous intensity (candela), but the course emphasizes these five fundamental units.

Derived Units: How They Are Built

• Derived units are formed by combining fundamental units through arithmetic operations.
• Key examples:
  • Force:
  • Formula: $F = m a$
  • SI unit for force: $1\ \text{N} = 1\ \text{kg}\cdot \text{m}/\text{s}^2$
  • Speed:
  • Formula: $v = \frac{dx}{dt}$
  • Unit: $\text{m/s}$
  • Volume:
  • Formula: $V = l \cdot w \cdot h$
  • Unit: $\text{m}^3$
• These relations illustrate how common physical quantities inherit their units from the base units.

Trace the Units: SIDETECTIVE Activity

• Objective: Trace the Units!
• Tasks:
  • Classify SI units as fundamental (base) vs. derived
  • Analyze physical formulas to identify which base units are involved
  • Apply unit conversions and perform dimensional analysis on real-world problems
• Importance: Develop a habit of checking dimensional consistency in equations and calculations.

Did you know? Insights about SI

• The SI system is the standard system used by scientists and most countries worldwide.
• It is logical and base-10, which simplifies conversions.
• The United States is one of the few countries that still widely uses English units in everyday life and some scientific contexts.

Practical Takeaways for the Course

• Always identify the quantity you are dealing with and its associated unit.
• Remember the seven base SI units and their symbols:
  • Length: m
  • Mass: kg
  • Time: s
  • Electric current: A
  • Temperature: K
  • Amount of substance: mol
  • Luminous intensity: cd
• Recognize that most quantities you encounter will be derived units; know at least the main examples: N, m, s, m^3, m/s, etc.
• Use dimensional analysis to verify formulas and unit consistency in problem solving.

Quick Reference Equations and Units

• Force relation:
  • $F = m a$
  • $1\ ext{N} = 1\ \text{kg} \cdot \text{m}/\text{s}^2$
• Speed relation:
  • $v = \frac{dx}{dt}$
  • Unit: $\text{m/s}$
• Volume relation:
  • $V = l \cdot w \cdot h$
  • Unit: $\text{m}^3$
• Base units recap:
  • Length: $\text{m}$
  • Mass: $\text{kg}$
  • Time: $\text{s}$
  • Electric current: $\text{A}$
  • Temperature: $\text{K}$
  • Amount of substance: $\text{mol}$
  • Luminous intensity: $\text{cd}$