Derived Units
Learning Objectives
- Students will understand how derived units are formed from base units
- Students will be able to identify common derived units (newton, joule, watt, pascal, hertz)
- Students will write derived units in terms of base units
Core Concepts
- Derived units are combinations of base units
- Common derived units: newton (N), joule (J), watt (W), pascal (Pa), hertz (Hz)
- Dimensional analysis with derived units
Formulas
$$\text{N} = \text{kg} \cdot \text{m/s}^2$$
Newton is the unit of force
$$\text{J} = \text{kg} \cdot \text{m}^2\text{/s}^2$$
Joule is the unit of work and energy
$$\text{W} = \text{J/s} = \text{kg} \cdot \text{m}^2\text{/s}^3$$
Watt is the unit of power
$$\text{Pa} = \text{N/m}^2 = \frac{\text{kg}}{\text{m} \cdot \text{s}^2}$$
Pascal is the unit of pressure
$$\text{Hz} = \frac{1}{\text{s}} = \text{s}^{-1}$$
Hertz is the unit of frequency
Units
| newton | N |
| joule | J |
| watt | W |
| pascal | Pa |
| hertz | Hz |
Interesting Fact
The hertz is named after Heinrich Hertz, who demonstrated electromagnetic waves
Key Scientist
James Prescott Joule
Joule studied energy; the joule unit measures work and energy
Modern Research
Modern particle physics introduces derived units like the electron-volt (eV) for convenience. In computational physics, natural units are often used where the speed of light (c), the reduced Planck constant (ℏ), and other fundamental constants are set to 1 for simplicity. This allows equations to be written in a more compact form without the need to include these constants explicitly.
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