Physics Measurement Basics

Measurement in Physics

• Physics begins with measurement, defined as a comparison with a standard.
• Measurement types include Metric and English systems, indicating different units of measure.
• Physical quantity refers to a quantifiable property of phenomena, bodies, or substances.

Units of Measurement

• Derived units result from mathematical combinations of SI base units, such as volume and energy.
• Acceleration is an example of a derived unit.
• Fundamental quantities form a subset of physical quantities, with each being irreducible to others.

Types of Errors

• Systematic errors arise from instruments or processes leading to consistent inaccuracies.
• Random errors are unusual deviations that occur unpredictably.

Scalar and Vector Quantities

• Scalars are quantities characterized only by magnitude.
• Vectors include both magnitude and direction, described with units.

Determining Vector Direction

• Vectors can be categorized based on quadrants and their corresponding signs:
  • Quadrant 1: (+,+) - North of East
  • Quadrant 2: (+,-) - North of West
  • Quadrant 3: (-,-) - South of West
  • Quadrant 4: (-,+) - South of East

Vector Addition

• The resultant of multiple vectors is obtained through graphical or analytical methods.

Graphical Method

• Uses Head to Tail and Tail to Tail methods to position vectors for summation.

Analytical Method

• Vectors in the same direction are summed arithmetically.
• Vectors in opposite directions are subtracted, considering the larger magnitude.
• Vectors at right angles utilize the Pythagorean theorem: c² = a² + b².
• Trigonometric methods:
  • Tan angle calculation: Tan^-1 (fy/fx).
  • Cosine Law: c² = a² + b² - 2ab cos(c).
  • Sine Law: a/sinA = b/sinB = c/sinC.

Component Method for Vector Addition

• Formulas for resolving vectors:
  • Vx = V cos(θ)
  • Vy = V sin(θ)
• Steps to using the component method:
  • Resolve the vector into horizontal (x) and vertical (y) components.
  • Sum x and y components to determine resultant.
  • Apply Pythagorean theorem: R² = Rx² + Ry².
  • Use signs of Rx and Ry to find the quadrant.
  • Compute the reference angle to clarify direction.