Lesson Plan: Dimensional Analysis Physics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to determine the dimensions of physical quantities given the relation between those quantities and other known quantities.

Objectives

Students will be able to

  • recognize that a quantity can be described in terms of its dimensions,
  • recognize that while a quantity can be measured using lots of different units, it always has the same dimensions,
  • recall the symbols for four of the basic dimensions: mass (๐‘€), length (๐ฟ), time (๐‘‡), and current (๐ผ),
  • determine the dimensions of common quantities using their defining formulae:
    • area = length๏Šจ,
    • volume = length๏Šฉ,
    • speed = lengthtime,
    • acceleration = lengthtime๏Šจ,
    • momentum = mass ร— velocity,
    • force = momentumtime,
    • charge = current ร— time,
    • frequency = 1time,
  • carry out algebraic manipulations of dimensional expressions,
  • understand dimension notation: [๐‘Ž]=๐‘€๐ฟ๐‘‡๐ผ๏ต๏ถ๏ท๏บ,
  • determine the dimensions of a quantity given a formula for that quantity and the dimensions of the identifiers in that formula,
  • recall what units relate to what dimensions,
  • convert between a unit expression and a dimension expression.

Prerequisites

Students should already be familiar with

  • the SI units for length, area, volume, speed, velocity, acceleration, momentum, force, charge, current, frequency, and time,
  • the formulae for various common physical quantities:
    • area = length๏Šจ,
    • volume = length๏Šฉ,
    • speed = lengthtime,
    • acceleration = lengthtime๏Šจ,
    • momentum = mass ร— velocity,
    • force = momentumtime,
    • charge = current ร— time,
    • frequency = 1time.

Exclusions

Students will not cover

  • the base quantities: thermodynamic temperature (๐œƒ), amount of substance (๐‘), luminous intensity (๐ฝ), or any algebraic manipulations of them.

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