2.1.3 Dimensional Analysis

• What is dimensional analysis used for in physics?

  Analyzing dimensions of quantities
• How can dimensional analysis be used to derive new equations?

  By deducing their form
• Dimensional analysis can help deduce the form of new equations based on dimensions.

  True
• What skills does dimensional analysis enhance in physics?

  Problem-solving skills
• Match the fundamental dimension with its symbol and unit:

  Length ↔️ L ||| meter (m)

  Mass ↔️ M ||| kilogram (kg)

  Time ↔️ T ||| second (s)

  Temperature ↔️ Θ ||| kelvin (K)
• Match the fundamental dimension with its symbol:

  Length ↔️ L

  Mass ↔️ M

  Time ↔️ T
• Dimensional analysis ensures the dimensions on both sides of an equation match
• To derive the period of a simple pendulum, dimensions can guide us to sqrt(l/g)
• Converting 60 mph to m/s requires using the conversion factor 1 mile = 1609.34 meters
• Match the fundamental dimension with its symbol and unit:

  Length ↔️ L, meter (m)

  Mass ↔️ M, kilogram (kg)

  Time ↔️ T, second (s)

  Temperature ↔️ Θ, kelvin (K)

  Electric Current ↔️ I, ampere (A)

  Luminous Intensity ↔️ J, candela (cd)

  Amount of Substance ↔️ N, mole (mol)
• Match the physical quantity with its dimensions:

  Area ↔️ L²

  Volume ↔️ L³

  Velocity ↔️ LT^-1

  Force ↔️ MLT^-2
• The principle of homogeneity states that the dimensions on both sides of an equation must be identical
• The equation for the period of a simple pendulum derived using dimensional analysis is T = 2π√(l/g)


  True
• What is the dimension of velocity?

  [LT^-1]
• The equation [LT^-1] = [LT^-1] confirms the consistency of the dimensions.


  True
• Dimensional analysis improves understanding of physical quantities and their relationships.


  True
• What are the relevant dimensions for the period T of a simple pendulum?

  [L^a g^b]
• Dimensional analysis is useful when the underlying physics is not fully known.


  True
• Match the uses of dimensional analysis with their descriptions:

  Check the validity of equations ↔️ Ensure dimensions match

  Derive new equations ↔️ Deduce form from dimensions

  Convert between units ↔️ Determine conversion factors
• One key benefit of dimensional analysis is ensuring equation validation.
• How many meters are there in 1 mile?

  1609.34
• Fundamental dimensions cannot be expressed in terms of each other.

  True
• The principle of homogeneity states that an equation is dimensionally consistent if each term on both sides has the same dimensions.

  True
• The constant in the period formula of a simple pendulum is derived experimentally and is equal to 2π.


  True
• Dimensional analysis is the process of analyzing the dimensions of physical quantities to determine their relationships.
• Dimensional analysis helps determine conversion factors between different units of the same physical quantity.
• Dimensional analysis determines conversion factors between different units of the same quantity.
• How many fundamental dimensions are there in physics?

  7
• What is the unit of length in the SI system?

  Meter
• Fundamental dimensions can be expressed in terms of each other.

  False
• What is one benefit of dimensional analysis?

  Equation validation
• What is the conversion factor between miles and meters?

  1 mile = 1609.34 meters
• Dimensional analysis is useful for validating equations, simplifying unit conversions, and enhancing problem-solving skills


  True
• Fundamental dimensions cannot be expressed in terms of each other and are universally accepted for dimensional analysis


  True
• The dimension of pressure is ML^-1T^-2
• Applying the principle of homogeneity ensures that an equation is dimensionally consistent


  True
• Steps to check equation consistency using dimensional analysis:

  1️⃣ Identify the dimensions of each variable

  2️⃣ Substitute the dimensions into the equation

  3️⃣ Simplify the dimensions on both sides

  4️⃣ Compare the dimensions to ensure they match
• The dimension of distance is [L]
• What is one key benefit of dimensional analysis?

  Validating equations
• What is the first step in using dimensional analysis to derive a formula?

  Identify relevant dimensions