Learning Outcomes
i. Define derived units and explain their relationship to base units.
ii. Analyze the physical quantities involved in a derived unit and represent it as a product or quotient of the base units.
iii. Understand the dimensional analysis method for expressing derived units and apply it to various examples.
Introduction
In physics, we measure various physical quantities, such as length, mass, time, velocity, acceleration, force, and energy. These quantities can be classified into two categories: base units and derived units.
Base units are the fundamental units of measurement that cannot be further broken down into simpler units. In the International System of Units (SI), there are seven base units:
Derived units are units that are formed by combining base units. For example, the unit of velocity is meters per second (m/s), which is a combination of the base units of length (meter) and time (second).
i. Expressing Derived Units from Base Units
There are two main methods for expressing derived units from base units:
Dimensional analysis: This method involves analyzing the physical quantities involved in a derived unit and representing it as a product or quotient of the base units. For example, the unit of force is newton (N), which is defined as kilogram meter per second squared (kg m/s²). This means that one newton is equal to the force that will accelerate a mass of one kilogram at a rate of one meter per second squared.
Formula substitution: This method involves substituting the base units into a physical formula that defines the derived unit. For example, the unit of energy is joule (J), which is defined as kilogram meter squared per second squared (kg m²/s²). This means that one joule is equal to the work done by a force of one newton acting over a distance of one meter.
Examples
Expressing derived units from base units is an important skill in physics. It allows us to understand the relationship between different physical quantities and to make accurate measurements.