Physical quantities
A 125-million-dollar mistake
- In 1999, NASA lost the Mars Climate Orbiter at Mars.
- One team used pounds, the other used newtons — and nobody converted.
- The spacecraft flew too low and burned up.
- It was a unit mistake, not a maths mistake.
What is a physical quantity?
- In physics we measure things.
- Every measurement is a physical quantity.
It always has two parts
- A quantity = a magnitude (the number) + a unit.
- The magnitude says how much; the unit says of what.
Every physical quantity has two parts: a number (its ____) and a unit.
The two parts are the magnitude (the number) and the unit.
A number alone means nothing
- "The speed is 90" — 90 what?
- $90\ \dfrac{\text{km}}{\text{h}}$, $90\ \dfrac{\text{m}}{\text{s}}$ and 90 mph are all different.
- Always write the unit too.
Saying "the speed is 90" — with no unit — gives a complete physical quantity.
Without a unit the number is ambiguous. "$90\ \dfrac{\text{km}}{\text{h}}$" is complete; "90" is not.
"$90\ \dfrac{\text{km}}{\text{h}}$" is a complete quantity. "90" on its own is not.
Which statement gives a complete physical quantity?
A physical quantity needs both a magnitude (the number, 70) and a unit (kg). A number alone, or a unit alone, is not enough.
Estimate everyday sizes
- You should know roughly how big common things are.
- Learn these standard values by heart.
Select all the estimates that are about right.
All are right except the speed of sound: in air it is about $340\ \dfrac{\text{m}}{\text{s}}$. $3 \times 10^{8}\ \dfrac{\text{m}}{\text{s}}$ is the speed of light.
How to estimate
- Compare with something you know (a person $\approx 70\ \text{kg}$).
- Round to one figure — a car is about $1000\ \text{kg}$, not $1043$.
- Getting the power of ten right matters most.
Estimate the acceleration of free fall $g$ near the Earth's surface.
Near the Earth's surface $g \approx 9.81\ \dfrac{\text{m}}{\text{s}^2}$ — roughly $10\ \dfrac{\text{m}}{\text{s}^2}$.
Order of magnitude
- A good estimate has the right power of ten.
- $70\ \text{kg}$ ✓ · $7\ \text{kg}$ ✗
Put these masses in order, smallest first.
Ordering by size checks your sense of order of magnitude: $0.1\ \text{kg}$, then $1\ \text{kg}$, then $70\ \text{kg}$.
The scale of the universe
- The same idea runs from an atom to the Sun.
- Each step along the line is ten times bigger.
You've got it
- a physical quantity = a magnitude + a unit
- learn the standard estimates (human, apple, sound, light, $g$)
- a good estimate has the right order of magnitude
Next — the SI units these are all built from.