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01

The expert's toolkit: SI units, defining constants and unit checks

In simple words

Rulers, clocks and scales all over the world agree because everyone uses the same set of units, tied to numbers in nature that never change. A good tutor uses those units carefully and checks every answer by asking: do the units make sense?

Before this course: Mechanics & Energy Models: modelling (course 15.3.3). You should be able to build and test models (Euler simulation, drag, springs, pendulums, orbits and energy budgets). In this course you learn to teach all of that to others, and to check other people's physics the way a professional does.

Key facts

The revised SI (NIST): a vote on 16 November 2018 in Versailles, France, changed the International System of Units, and the change went into effect on 20 May 2019. The kilogram, kelvin, ampere and mole were redefined in terms of constants of nature.
The seven defining constants (exact values, NIST):

Constant	Symbol	Exact value
Caesium-133 hyperfine frequency	ΔνCs	9 192 631 770 Hz
Speed of light in vacuum	c	299 792 458 m/s
Planck constant	h	6.626 070 15 x 10^-34 J s
Elementary charge	e	1.602 176 634 x 10^-19 C
Boltzmann constant	k	1.380 649 x 10^-23 J/K
Avogadro constant	N_A	6.022 140 76 x 10^23 per mole
Luminous efficacy	K_cd	683 lm/W

Standard gravity g_n = 9.806 65 m/s^2 is also exact (NIST, CODATA 2022). It is a defined reference value; real local gravity differs a little, as you saw in course 15.3.3.
Writing units like a professional (NIST checklist, examples):

Write	Not	Rule
75 cm	75 cms	Unit symbols have no plural
5 s	5 sec	No home-made abbreviations
a 25 kg ball	a 25-kg ball	A space between number and unit
(123 ± 2) g	123 ± 2 g	Make clear which unit the whole value has
15 739.012	15,739.012	Group digits with thin spaces, not commas

Mass is not weight. NIST's checklist reminds writers that weight is a force (in newtons), while in everyday speech "weight" often means mass (in kilograms). A tutor says which one is meant.
Unit (dimension) checks catch wrong powers, not missing numbers. For a pendulum, T = 2π x square root of (L / g) has units square root of (m / (m/s^2)) = s, which is correct. If a learner writes v = 2gh, the units are m^2/s^2, not m/s, so the formula must be wrong. But if a learner forgets the 2 in t = square root of (2h / g), the units still work: for h = 1.0 m they get 0.32 s instead of 0.45 s (checked with Python). Unit checks are necessary, not sufficient.

Step by step

Print or copy the table of seven defining constants and the five writing rules.
Take three worked solutions from your notes for courses 15.3.2 or 15.3.3.
Circle every number that has no unit, and every unit written against the NIST rules.
For each final formula, write the units of each side and check they match.
For each answer, also do a size check (is 0.45 s for a 1 m drop reasonable?), because units alone cannot catch a missing factor.
Rewrite one solution as a "model answer" a learner could copy the style of.
Check: every quantity in your model answer has a correct unit, and both sides of every equation have the same units.

Watch on YouTube

Intro to dimensional analysisKhan Academy India - English · YouTube · youtube.com

Videos by other creators on YouTube, for reference. They are not made by or affiliated with The Future Market.

LESSON 01The expert's toolkit: SI units, defining constants and unit checks

LESSON 01 / ANIMATED LESSON / AI VOICE00:00 / 01:15

Voice

Read the video script

[Host holding a ruler and a phone stopwatch] "Every ruler and clock on Earth agrees, because they all point back to the same seven numbers."
[Text on screen: since 20 May 2019, the SI rests on seven exact constants] "Since May 2019, the SI has been built on seven exact constants of nature, such as the speed of light and the Planck constant."
[Screen: "75 cms" crossed out, "75 cm" written] "As a tutor, write units properly. No plural on symbols, and a space between the number and the unit."
[Text on screen: v = 2gh gives m^2/s^2, not m/s] "Then check units. If the two sides do not match, the formula is wrong."
[Host] "But careful: units cannot catch a missing 2. Always do a size check as well."

Try it now

A learner writes: "The 2-kg ball fell 5 meters in 1 secs, so its speed was v = gh = 49 m/s." List every problem you can find (units, style, physics, size) and write a short, kind correction. (Hints: unit writing, the units of gh, and whether 49 m/s is reasonable after a 5 m fall.)

ClaudeStuck? Copy a ready-made prompt for Claude

Copy this, open Claude, paste it, and Claude will walk you through the lesson step by step.

For a grown-up: Claude is for adults (18+). Copy this, paste it into Claude, and use the answer to explain the lesson to your child.

I'm learning "Physics Tutor: teach" on The Future Market. Lesson 1: "The expert's toolkit: SI units, defining constants and unit checks".

What the lesson teaches:
- The revised SI (NIST): a vote on 16 November 2018 in Versailles, France, changed the International System of Units, and the change went into effect on 20 May 2019. The kilogram, kelvin, ampere and mole were redefined in terms of constants of nature.
- The seven defining constants (exact values, NIST):
- Constant - Symbol - Exact value
- Caesium-133 hyperfine frequency - ΔνCs - 9 192 631 770 Hz
- Speed of light in vacuum - c - 299 792 458 m/s
- Planck constant - h - 6.626 070 15 x 10^-34 J s
- Elementary charge - e - 1.602 176 634 x 10^-19 C

The exercise I'm working on:
A learner writes: "The 2-kg ball fell 5 meters in 1 secs, so its speed was v = gh = 49 m/s." List every problem you can find (units, style, physics, size) and write a short, kind correction. (Hints: unit writing, the units of gh, and whether 49 m/s is reasonable after a 5 m fall.)

I'm stuck. Please:
1. Explain the main idea in plain, simple words with one everyday example.
2. Walk me through the exercise one small step at a time. Ask me what I've done so far before giving the next step.
3. Don't just give me the final answer. Help me do it myself, and check my work when I share it.

I'm a parent helping my child (about 8 years old) with a lesson called "The expert's toolkit: SI units, defining constants and unit checks" from the course "Physics Tutor: teach".

Here's what the lesson says:
Rulers, clocks and scales all over the world agree because everyone uses the same set of units, tied to numbers in nature that never change. A good tutor uses those units carefully and checks every answer by asking: do the units make sense?

The activity:
A learner writes: "The 2-kg ball fell 5 meters in 1 secs, so its speed was v = gh = 49 m/s." List every problem you can find (units, style, physics, size) and write a short, kind correction. (Hints: unit writing, the units of gh, and whether 49 m/s is reasonable after a 5 m fall.)

Please explain this so an 8-year-old understands: short sentences, a fun everyday example, and no hard words.
Then give me 3 simple questions I can ask my child to check they understood, and a way to do the activity together, one tiny step at a time.

Open Claude

Sources

NIST, Meet the constants: www.nist.gov/si-redefinition/meet-constants
NIST, SI redefinition (vote and effective date): www.nist.gov/si-redefinition
NIST, Standard acceleration of gravity (CODATA 2022): physics.nist.gov/cgi-bin/cuu/Value?gn
NIST, Checklist for reviewing manuscripts (SI style rules): physics.nist.gov/cuu/Units/checklist.html

My notes

I learned this

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