Units and Measurement

Measurement and Vectors

• This section covers systems of measurement and vector addition.
• It emphasizes understanding physical quantities, base quantities, prefixes, orders of magnitude, and scalar/vector quantities.
• Also covers determination of resultant vectors via graphical methods.

Systems of Measurement

• Science uses both qualitative and quantitative observations.
• A quantitative observation is a "measurement" and requires both a number and a unit.
• Standard measurement systems are necessary for scientists to communicate effectively.
• The English system is mainly used in the United States.
• The metric system is used by most of the industrialized world.
• The International System (SI) was established in 1960 and is based on the metric system.

Measurement

• Mass, measured in kilograms (kg)
• Length, measured in meters (m)
• Time, measured in seconds (s)
• Temperature, measured in kelvin (K)
• Electric current, measured in ampere (A)
• Amount of substance, measured in mole (mol)
• Luminous intensity, measured in candela (cd)

Basic Types of Quantity

• Fundamental quantities are basic and measured by direct methods.
• Fundamental units are assigned to fundamental quantities.
• Meter, kilogram, and second (MKS) units are standard for length, mass, and time.
• Centimeter, gram, and second (CGS) units are used for smaller quantities.
• Derived quantities result from combining fundamental quantities through operations.
• Examples of derived quantities include area (square meter), volume (cubic meter) and density (kilogram per cubic meter).
• Physical quantities are classified as base or derived.

The SI System

• Measurements are easily understood by all scientists, so the SI system is used worldwide.
• Measurements are easier to convert than the English system.
• Each base quantity has a corresponding unit.
• Length uses meters (m)
• Mass uses kilograms (kg)
• Time uses seconds (s)
• Electric current uses amperes (A)
• Temperature uses kelvin (K)
• Amount of substance uses moles (mol)
• Luminous intensity uses candelas (cd)

Derived Quantities

• Area is length multiplied by width and is measured in m².
• Volume is length × width × height and is measured in m³.
• Density is mass ÷volume and is measured in kgm⁻³.
• Speed is distance ÷ time and is measured in ms⁻¹.
• Acceleration is a change in velocity ÷ time and is measured in ms⁻².
• Force is mass × acceleration and is measured in kgms⁻².
• Pressure is force ÷ area and is measured in Nm⁻².
• Work is force × distance and is measured in Nm.
• Power is work ÷ time and is measured in Nms⁻².

Basic measurements include:

• Length is the distance between objects and is measured in meters.
• Mass is the amount of matter in an object and is measured in grams. 1 pound equals 454 grams.
• Volume is the space that something takes up and is measured in liters for liquids. 1 ml is equal to 1 cm³.
• Temperature is measured in Celsius (ranges from 0 for freezing to 100 for boiling) or Kelvin. To convert to Kelvin add 273 degrees to the Celsius reading.

Measurement System Comparisons:

• Length is measured in Yard/Inch (English) and Meter/Centimeter (SI system).
• Mass is measured in Ounce/Pound (English) and Gram/Kilogram (SI System).
• Volume is measured in Quart (English) and Liter (SI System).
• Temperature is measured in Fahrenheit (English) and Celsius/Kelvin (SI System).
• Time is measured in Second (English) and Second (SI System).
• All measurement systems have standards, which are exact quantities agreed upon for comparison.

Prefixes

• Nano (n) represents 10⁻⁹
• Micro (μ) represents 10⁻⁶
• Milli (m) represents 10⁻³
• Centi (c) represents 10⁻²
• Deci (d) represents 10⁻¹
• Kilo (k) represents 10³
• Mega (M) represents 10⁶
• Giga (G) represents 10⁹

Metric Measurement: Length

• Length is the distance between two points, regardless of width, height, or depth.
• The basic unit of length in the SI system is the meter.
• One meter is about the same as the length of the English yard (3 feet).
• Area is a length measurement, found by Length x Width, and expressed in units squared.

Metric Measurement: Mass

• Mass measures the amount of matter in an object.
• The basic unit of mass is the gram.

Metric Measurement: Volume

• Volume measures the amount of space something takes up.
• The basic unit for volume is the liter, and it is generally used for liquids.
• Volumes: L x W x H (cm x cm x cm = cm³)
• Objects that do not have a definite length like and irregular shaped item, use water replacement to determine volume.
• NOTE: 1 ml = 1 cm³

Metric Measurement: Temperature

• Temperature measures the kinetic energy of atoms in an object.
• Temperature is measured with a thermometer in Celsius or Kelvin.
• Celsius ranges from 0 (freezing) to 100 (boiling).
• To convert to Kelvin, you add 273 degrees to the Celsius value.
• Freezing in Kelvin is 273 K, boiling is 373 K.

Scalars and Vectors

• Scalar quantities have magnitude only.
• Scalar quantities are added or subtracted using simple arithmetic.
• Example: 4 kg + 6 kg = 10 kg
• Vector quantities have both magnitude and direction.
• Magnitude = 100 N
• Direction = Left

Examples of Scalars

• Distance
• Speed
• Mass
• Time
• Pressure
• Energy
• Volume
• Density

Examples of Vectors

• Displacement
• Velocity
• Weight
• Acceleration
• Force
• Momentum

Vector Addition

• Parallel vectors can be added arithmetically.
• Vector addition is used in physical quantities where vectors represent velocity, displacement, and acceleration.
• Vectors can be added geometrically by positioning their tails together and forming a parallelogram, where the sum is the diagonal starting from the tails' intersection.
• Vectors added together in two ways to get a result, are commutative.
• When adding vectors, they must have the same units and be of analogous quantities.
• Vector subtraction is adding a negative vector: A - B = A + (-B)

Displacement

• Change is the position of an object.
• It is a vector quantity, therefore, you must know how far something is going and in which direction.
• Walking a same distance from your front door will not get you to the same place if you walk in different directions.
• Displacement is a straight arrow from start to end, regardless of the path.
• Total displacement for a round trip is 0.

Test your knowledge on derived and fundamental quantities. Explore the importance of the SI system and the CGS system. Understand qualitative and quantitative observations.