How To Use Dimensional Analysis To Find The Units of a Variable

TL;DR

This video explains how to use dimensional analysis to find the units of variables in equations.

Transcript

in this video we're going to focus on dimensional analysis finding the units of a variable so typically you'll be given an equation this equation is the force of gravitation whenever you have two objects particularly massive planetary size objects there's going to be a force of gravity that attracts them to each other for example let's say this is ... Read More

Key Insights

• 🇦🇪 Dimensional analysis is a tool used to find the units of variables in equations, ensuring mathematical correctness and meaningful units.
• 🇦🇪 By rearranging equations and plugging in the units of known variables, we can determine the units of unknown variables.
• ❎ The gravitational constant, g, has units of newtons times meters squared per kilogram squared.
• ❎ The energy variable, e, in Einstein's equation has units of kilograms times meters squared per second squared.
• 🫢 The gas constant, r, in the ideal gas law equation has units of liters times atm per moles times kelvin.
• 🥵 The specific heat capacity, c, has units of joules per gram per Celsius degree in the calorimetry equation.
• ❎ Coulomb's law equation has the constant, k, with units of newtons times meters squared per coulomb squared.

Summary & Key Takeaways

• The video discusses dimensional analysis and how to find the units of variables in equations.

• It explains the process of solving for the units of the gravitational constant in the force of gravitation equation.

• The video also demonstrates how to find the units of the energy variable in Einstein's famous equation and the gas constant in the ideal gas law equation.

• It further explores finding the units of the specific heat capacity in the calorimetry equation and the constant in Coulomb's law equation.

• The video concludes by explaining how to find the units of the rate constant in a rate law expression.