Once upon a time, in the late 1990s — when many of you hadn’t even been born yet, and even your parents might have been your age back then 😄.
Back then, I was one of those people who was obsessed with NASA’s space activities. I went to every astronomy book, magazine, and seminar I could get my hands on. The internet wasn’t anything like it is today either — you had to go to the central library of the Theoretical Physics Group or somewhere that had internet just to load a single page. It wasn’t like now, where you have everything at your fingertips on your phone in two seconds.
Well, NASA had a dreamy Mars project — they had launched two spacecraft together: one was supposed to land on Mars and become a ground laboratory, while the other was supposed to orbit Mars and send data from the surface back to Earth — it was a new system. Launching a spacecraft to Mars isn’t like sending a package today and having it arrive tomorrow — damn, it takes 4 months to get there! So after the launch, I started counting the days. I’m serious, I was going crazy with anticipation.
Finally, the first spacecraft arrived:
Whooooo! 🎉 Let’s see what happens…
Suddenly, NASA announced: “After landing, the spacecraft has been lost.” 😐
Shortly after, confirmation came: The spacecraft crashed into the surface of Mars. 🛰️🔥
Well, I said, okay. The second spacecraft, the Mars orbiter, is still on its way. When it arrives and orbits Mars, at least we’ll find out what happened.
The second spacecraft arrived… NASA announced: The second spacecraft is also lost. It probably did not enter orbit. 😶
So all my ships sank at once. I was depressed, just staring at the horizon during my classes. What’s the point of life anyway? How many more years until the next spacecraft goes to Mars?
So, what was the lesson from this disaster? 💥
A few months later, NASA announced the real reason:
NASA’s team calculated the launch phase up to Mars using SI (metric) units. However, the manufacturer’s team worked on the landing and Mars orbit phases using English units. They didn’t convert the numbers. That’s it.
It was that simple. Two spacecraft, hundreds of millions of dollars, years of work — all lost due to a “forgotten” unit conversion. I barely held myself back from protesting in front of the British embassy 😅.
The lesson: Start your calculations and measurements with one unit system and stick with it to the end. If you used a different system somewhere — convert everything before continuing. That common system the rest of the world uses? It’s SI.
Where did the problem start? 🤔
Imagine if every city and country had its own unit of measurement. One person measures in “inches,” another in “yards,” and another in “feet.” Trade, science, and engineering — everything would fall apart! Because my unit differs from yours, and no one understands what the other is saying.
For this reason, a good unit of measurement must have two important characteristics: 1. It must not change (it must be the same size everywhere and always) 2. It must be reproducible (anyone, anywhere in the world, must be able to recreate it exactly)
From the mid-nineteenth century, the need for a global scale system became completely clear. Countries came together and signed a treaty called the “Metre Convention.” Interestingly, Iran is also a member of this convention! 🇮🇷 And the Metrology Center of the National Standards Organization of Iran is our country’s link to this global system.
What is the SI system? 📐
The system that almost everyone in the world (scientists and engineers) uses today is called the International System of Units, commonly abbreviated as SI (from the French phrase Système International). It was previously known as the “metric system.”
The genius idea behind SI is this: instead of defining thousands of separate units for thousands of physical quantities (which would be a nightmare 😵), we select just seven base quantities and derive the units for all other quantities from these seven!
The Seven SI Base Units 🏛️
These are the main pillars of the entire system. Everything else is built from these seven:
> 🎮 **Click on each card** to learn what each unit is and how it is defined.
| Quantity | Unit Name | Symbol |
|---|---|---|
| Length | Meter | m |
| Mass | Kilogram | kg |
| Time | Second | s |
| Temperature | Kelvin | K |
| Amount of Substance | Mole | mol |
| Electric Current | Ampere | A |
| Luminous Intensity | Candela | cd |
An interesting point is that these seven were chosen to be independent of each other — meaning none of them can be derived from the others. It’s like the seven basic notes in music, which can be combined to create countless songs 🎵.
Derived Units: The Children of the Seven Base Units 👶
Now here is the beauty of it. The other units (known as derived units) are constructed from these same seven. For example?
Remember in 9th-grade science, we defined speed like this: distance divided by time. Well, distance is a measure of length (unit: meter), and time is measured in seconds. So, the unit of speed naturally becomes meters per second (m/s) — a derived unit built from two base units! 🎉
Some commonly used derived units are so important that they were given a specific name:
| Quantity | Unit Name | In Terms of Base Units |
|---|---|---|
| Force | Newton (N) | kg·m/s² |
| Pressure | Pascal (Pa) | kg/(m·s²) |
| Energy | Joule (J) | kg·m²/s² |
These specific names (often taken from great scientists, like Newton, Joule, and Pascal) are just for convenience in speech and writing. Instead of constantly saying “kilogram meter per second squared,” we say “Newton.” Easier, right? 😄
💡 Teacher’s Tip: As someone who has taught and studied for years, I recommend always memorizing derived units alongside their base units. That is, when you say “Joule,” you should know in your mind that:
[ 1,text{J} = 1,frac{text{kg} cdot text{m}^2}{text{s}^2} ]
Now, look at this interesting connection: Joule = kilogram × meter² per second² = mass × (meter per second)² = mass × velocity². Oh, how close this is to kinetic energy: ( E_k = frac{1}{2}mv^2 )! In other words, the unit of the Joule comes directly from that formula.
This approach has three benefits: unit conversion becomes easier, you remember formulas better, and you can check the validity of your answers — if the units on both sides of the equation don’t match, you definitely made a mistake somewhere.
An Interesting Story: How Were These Units Defined? 📜
The definition of these units is itself a story full of ups and downs:
Meter: In the beginning (late 18th century), the meter was defined as one ten-millionth of the distance from the equator to the North Pole! 🌍 Later, they created a metal bar (platinum-iridium) and declared, “This bar is one meter.” But now? The meter is defined by the speed of light: the distance light travels in a vacuum in 1/299,792,458 seconds! 🤯 Why is this so strange? Because the speed of light is a universal constant that never changes — so the meter never changes either.
Kilogram: This one is even more interesting! Until 2019, the kilogram was defined by a real metal cylinder kept in the Sèvres Museum in France 🏛️. So, “one kilogram” meant “the mass of that cylinder.” But what was the problem? Over time, the cylinder’s mass changed slightly! 😬 That’s why, in 2019, the kilogram was redefined based on a fundamental constant of nature (Planck’s constant).
Second: In the past, the second was defined based on the solar day (1/86,400 of a day). Now? It’s defined by atomic clocks that are so precise they only drift by one second after several million years! ⏱️
Do you see the pattern? Science is moving toward definitions tied to immutable constants of nature, rather than physical objects that might degrade. This is the “reproducibility” we mentioned at the start of the lesson 🎯.
The standard kilogram cylinder — made of platinum-iridium alloy, kept inside three glass covers (Image: NIST, Public Domain)
Unit Conversion: The “Multiply by One” Trick 🔄
Here you’ll learn a practical skill that will stay with you throughout your physics studies. Often, you need to change the unit of a quantity (for example, from centimeters to meters, or from kilometers per hour to meters per second).
What’s the trick? We use something called a conversion factor — which is actually a fraction that equals one. For example:
Since 100 centimeters = 1 meter, this fraction equals one:
[ frac{1,text{m}}{100,text{cm}} = 1 ]
And since multiplying anything by one doesn’t change its value, we can use it to change units! Example:
[ 85,text{cm} = 85,text{cm} times frac{1,text{m}}{100,text{cm}} = 0.85,text{m} ]
See what happened? The centimeters canceled out, leaving only meters 🎩✨. Here’s another example (converting kilometers per hour to meters per second):
[ 36,frac{text{km}}{text{h}} = 36 times frac{1000,text{m}}{3600,text{s}} = 10,frac{text{m}}{text{s}} ]
> 🎮 **Try it yourself:** Enter a number and change the units to see how the conversion works. For example, convert 36 kilometers per hour to meters per second!
Unit Consistency: Checking the Health of an Equation 🩺
A super useful trick: in any physics equation, the units on both sides must match. This is the best way to know if your answer is correct or if you made a mistake somewhere.
For example, Newton’s second law: ( F = ma ) (Force = Mass × Acceleration). The unit for mass is kilograms, and the unit for acceleration is m/s². So the unit on the right side becomes kg·m/s² — which is exactly a Newton! 🎯 So the equation is dimensionally consistent.
Golden tip 💡: Always convert units to SI before plugging in numbers (mass to kilograms, length to meters, etc.). This way, your answer will automatically come out in the correct unit, and you won’t make mistakes.
Unit Prefixes: When Numbers Are Very Large or Very Small 🔬🔭
Sometimes we deal with quantities that are either very large or very small. Writing “0.000001 meters” is both difficult and prone to errors. The solution? Prefixes!
Each prefix represents a power of ten that attaches to a unit. Here are a few common ones you should know by heart:
| Prefix | Symbol | Factor |
|---|---|---|
| Giga | G | 10⁹ |
| Mega | M | 10⁶ |
| Kilo | k | 10³ |
| Centi | c | 10⁻² |
| Milli | m | 10⁻³ |
| Micro | µ | 10⁻⁶ |
| Nano | n | 10⁻⁹ |
For example, 1 micrometer means 10⁻⁶ meters, or 1 kilogram means 10³ grams.
⚠️ Very important: Pay close attention to the capitalization of the symbols! For instance, M (Mega, uppercase) and m (milli, lowercase) are vastly different — one is 10⁶ and the other is 10⁻³! If you mix them up, your answer will be off by billions 😅.
Quick Summary 🎁
The SI system is a “universal common language” for measurement, built on seven base units. All other (derived) units are constructed from these seven. To convert units, we use conversion factors (which equal one), and we always check that the units on both sides of an equation are compatible. We also have prefixes for very large or very small numbers. That’s it! 😎
Did You Know? 💡
Ancient Iranians had their own units for measuring mass: khavar, man, sir, mithqal, chickpea, and wheat! 🌾 Yes, “wheat” and “chickpea” were actually units of weight — because the sizes of wheat and chickpea grains were relatively consistent and were used as references. (Don’t worry, you don’t need to memorize these for the exam 😄, it’s just interesting to see that our ancestors were also looking for the same “fixed reference” that the SI system uses today.)
Test Yourself 📝
Click on each question to reveal the answer 👇
* * *
Analysis with Python 🐍
Unit Conversion — Never Get It Wrong! 🔄
Remember the story of the spacecraft that turned into $327 million worth of smoke? A proper unit conversion system can prevent such disasters. Let’s turn Python into our unit conversion assistant:
import numpy as np
import matplotlib.pyplot as plt
# ── SI prefix table ──────────────────────────────────────────────
prefixes = {
'Tera (T)': 1e12,
'Giga (G)': 1e9,
'Mega (M)': 1e6,
'Kilo (k)': 1e3,
'--- base ---': 1,
'Centi (c)': 1e-2,
'Milli (m)': 1e-3,
'Micro (u)': 1e-6,
'Nano (n)': 1e-9,
'Pico (p)': 1e-12,
}
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 4.5))
names = list(prefixes.keys())
vals = list(prefixes.values())
colors = ['#e74c3c' if v >= 1 else '#3498db' for v in vals]
bars = ax1.barh(names, np.log10(vals), color=colors, alpha=0.8)
ax1.axvline(0, color='black', lw=1.5)
ax1.set_xlabel('Power of 10 (log₁₀)')
ax1.set_title('SI Prefixes — logarithmic scale', fontweight='bold')
for bar, v in zip(bars, vals):
w = bar.get_width()
label = f'x10^{int(np.log10(v))}' if v != 1 else 'x1'
ax1.text(w + (0.3 if w >= 0 else -0.3), bar.get_y() + bar.get_height()/2,
label, va='center', ha='left' if w >= 0 else 'right', fontsize=8)
ax1.grid(axis='x', alpha=0.3)
# km/h to m/s conversion
speeds_kmh = np.array([0, 30, 50, 60, 90, 100, 120, 140])
speeds_ms = speeds_kmh / 3.6
ax2.scatter(speeds_kmh, speeds_ms, color='#e74c3c', s=80, zorder=5)
ax2.plot(speeds_kmh, speeds_ms, 'b-', lw=1.5, alpha=0.6)
for kmh, ms in zip(speeds_kmh, speeds_ms):
ax2.annotate(f'{ms:.1f}', (kmh, ms), textcoords='offset points',
xytext=(4, 4), fontsize=8)
ax2.set_xlabel('Speed (km/h)'); ax2.set_ylabel('Speed (m/s)')
ax2.set_title('km/h to m/s conversionn(1 km/h = 1/3.6 m/s)', fontweight='bold')
ax2.grid(alpha=0.4)
plt.tight_layout()
plt.savefig('si_units.png', dpi=120, bbox_inches='tight')
plt.show()
# ── Unit consistency check (F = ma) ──────────────────────────────
print("Unit consistency check for F = ma:")
print(f" mass: kg | acceleration: m/s² | force = kg*m/s² = Newton (N)")
print(f" Example: m=2 kg, a=3 m/s² -> F = {2*3} N")🎯 Challenge: Convert the speed of sound (34
- International System of Units — Persian Wikipedia
- International System of Units — Wikipedia EN
- Mars Climate Orbiter — Wikipedia EN (That $327 million spacecraft!)
- Metric prefix — Wikipedia EN
Video — YouTube 🎬
- Veritasium: The kg is Changing — The redefinition of the kilogram in 2019
- Minute Physics: What is a Meter?
- Real Engineering: How NASA Lost a $327 Million Spacecraft
Video — Aparat 🎬
On this site 🔗
_In the next section, we’ll dive into a very practical topic:_Precision of measuring instruments — why no measurement is perfectly error-free, and how we can reduce errors 📏. See you there! 👋
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