Physical Quantities and Measurement Units

Physical Quantities

• A physical quantity can be measured and described by a magnitude and unit.
• Examples include: mass, length, area, temperature.

Units of Measurement

• A unit is the standard used to measure a physical quantity.
• Common systems of units include:
  • CGS system: Centimetre-Gram-Second
  • MKS system: Metre-Kilogram-Second
  • FPS system: Foot-Pound-Second
  • International System of Units (SI): the preferred system globally

International System of Units (SI)

• SI uses seven fundamental units and two supplementary units.
• Fundamental Units: Define the base quantities of the SI system.
  • Length: Metre (m) - defined as the distance travelled by light in a vacuum in 1/299,792,458 of a second.
  • Mass: Kilogram (kg) - defined by a platinum-iridium cylinder kept at the International Bureau of Weights and Measures.
  • Time: Second (s) - defined by the time taken for 9,192,631,770 oscillations of a cesium-133 atom.
  • Temperature: Kelvin (K) - the absolute temperature scale with 0 K being absolute zero.
  • Electric Current: Ampere (A) - defined as the constant current that, if maintained in two straight parallel conductors of infinite length and negligible circular cross-section placed one metre apart in vacuum, would produce between these conductors a force equal to 2 x 10^-7 Newton per metre of length.
  • Amount of Substance: Mole (mol) - the amount of substance that contains as many elementary entities as there are atoms in 0.012 kg of carbon-12.
  • Luminous Intensity: Candela (cd) - defined as the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 10^12 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.
• Supplementary Units: Refer to plane angle and solid angle.
  • Plane Angle: Radian (rad) - an angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
  • Solid Angle: Steradian (sr) - the solid angle subtended at the center of a sphere by its surface whose area is equal to the square of the radius of the sphere.

Dimensions

• The unique quality or type of every physical quantity that distinguishes it from all other quantities.
• Refers to the qualitative nature of a physical quantity.
• Examples:
  • Length: [L]
  • Mass: [M]
  • Time: [T]

Fundamental and Derived Dimensions

• Fundamental Dimensions: Measured independently and constitute the essential physical quantities (e.g., Length, Mass, Time).
• Derived Dimensions: Expresses other quantities as products or quotients of fundamental dimensions (e.g., Area, Volume, Force)

Dimensional Analysis

• A method to check the correctness of a physical equation.
• All terms in an equation must have the same dimensions; if they don't, the equation is incorrect.
• Can also be used to derive physical laws.

SI Prefixes

• Used to express very large or very small quantities.
• Examples:
  • milli (m): 10^-3
  • micro (µ): 10^-6
  • nano (n): 10^-9
  • pico (p): 10^-12
  • kilo (k): 10^3
  • mega (M): 10^6

Vector and Scalar Quantities

• Scalar Quantities: Measured with numbers and units only.
  • Examples: Length, Temperature, Time.
• Vector Quantities: Measured with numbers and units, and have a specific direction.
  • Examples: Acceleration, Displacement, Force.

Components of a Vector

• Any vector can be represented by its horizontal and vertical components.
• A vector A making an angle θ with the x-axis has:
  • Horizontal Component: Ax = A cosθ
  • Vertical Component: Ay = A sinθ

Sign Convention for Vectors

• The signs of a vector's components depend on the quadrant it's located in.
  • For example, if θ = 120°, Ax is negative and Ay is positive.

Unit Vector Notation

• A unit vector is a dimensionless vector with a magnitude of 1.
  • i: unit vector in the positive x direction.
  • j: unit vector in the positive y direction.
  • k: unit vector in the positive z direction.
• A vector A can be expressed as:
  • A = Ax i + Ay j + Az k
  • Ax i is a vector of magnitude |Ax| lying on the x-axis.
  • Ay j is a vector of magnitude |Ay| lying on the y-axis.
  • Az k is a vector of magnitude |Az| lying on the z-axis.

This quiz covers the essential concepts of physical quantities, including their definitions, measurements, and the various systems of units used. Learn about the International System of Units (SI) and its fundamental components. Perfect for students seeking to solidify their understanding of measurement in physics.