1.1Physical quantities and kinematics
Physical Quantities AND Units
5 min read 10 parts Lesson 2 of 22 1 quiz
Lesson summary
1.1 Physical Quantities and Units — AS PHYSICS 9702 notes: Use SI base and derived units, check homogeneity, handle uncertainties and add and resolve vectors.Every physical quantity is a numerical magnitude multiplied by a unit.Base quantities — mass (kg), length (m), time (s), c…
- Derived quantities
- Charge is derived
- What the symbols mean
- Prefixes scale units by powers of ten
- Areas and volumes
- To find the unit of a constant
Section 1 of 10Physical quantities
Every physical quantity is a numerical magnitude multiplied by a unit.
Base quantities
- Base quantities mass (kg), length (m), time (s), current (A) and temperature (K) are the five needed here;
- the mole is used later.
Derived quantities
- Derived quantities come from defining equations, for example force F = ma gives N = kg m s-2.
Charge is derived
- Q = It, so C = A s.What the symbols mean: Q = charge (C) · I = current (A) · t = time (s)
Section 2 of 10Derived units in base units
| Unit | Base units |
|---|---|
| newton (N) | kg m s-2 |
| joule (J) | kg m2 s-2 |
| watt (W) | kg m2 s-3 |
| pascal (Pa) | kg m-1 s-2 |
| coulomb (C) | A s |
| volt (V) | kg m2 s-3 A-1 |
Section 3 of 10Prefixes and estimates
1Prefixes scale units by powers of ten
- Prefixes scale units by powers of ten pico 10-12 up to tera 1012.
2Areas and volumes
- Areas and volumes the conversion factor is squared or cubed, so 1 m3 = 106 cm3.
3Estimates
- Estimates give 1 significant figure or an order of magnitude that is physically reasonable.
4
Mass of adult 70 kg, height of room 3 m, walking speed 1.5 m s-1, wavelength of visible light 5 × 10-7 m.
Section 4 of 10Checking homogeneity
1
Write the quantity to be checked as a formula of other quantities.
2
Replace every quantity by its SI base units.
3
Ignore pure numbers such as ½, 2 and π.
4
Combine the powers of each base unit using the index laws.
5
Compare the left side with each term on the right.
6
State the conclusion: homogeneous (possibly correct) or not homogeneous (definitely wrong).
Section 5 of 10Using homogeneity
Using homogeneity
To find the unit of a constant
- To find the unit of a constant rearrange to make the constant the subject, then substitute base units.
For drag F = kv2, k has units kg m-1.
A non-homogeneous equation is definitely wrong
- A non-homogeneous equation is definitely wrong a homogeneous one may still be wrong because numerical factors or missing terms cannot be checked.
Section 6 of 10Errors
Errors
Systematic errors
- Systematic errors zero errors, calibration errors, parallax always from the same side;
- they shift all readings one way and are removed by correcting the instrument or method, not by averaging.
Random errors
- Random errors fluctuating readings, human timing variation, parallax from varying angles; reduced by repeating and averaging,
- or by timing many oscillations.
A measurement can be precise but inaccurate
- A measurement can be precise but inaccurate or accurate but imprecise.
Section 7 of 10Uncertainties
1
Percentage uncertainty = (absolute uncertainty ÷ measured value) × 100%.
2Adding or subtracting
- Adding or subtracting add absolute uncertainties, Δ(a ± b) = Δa + Δb.
3Multiplying or dividing
- Multiplying or dividing add fractional or percentage uncertainties.
4For y
For y ambn ÷ c
- Δy ÷ y = mΔa ÷ a + nΔb ÷ b + Δc ÷ c; uncertainties always add, never subtract.
5Raising to a power
- Raising to a power fractional uncertainty of xn is |n| times that of x, so √x halves it.
6The uncertainty of a single reading
- The uncertainty of a single reading is often ± the smallest scale division,
- or half of it for analogue scales; for repeated readings use half the range.
7A length found from two ruler readings
- A length found from two ruler readings the uncertainties add.
8Quote the final uncertainty to 1 (occasionally 2) significant figures
- Quote the final uncertainty to 1 (occasionally 2) significant figures and round the value to the same decimal place.
Section 8 of 10Vectors
Vectors
Scalars have magnitude only
- Scalars have magnitude only vectors have magnitude and direction.
Add by a scale drawing
- Add by a scale drawing state a scale, draw tip to tail, and draw the resultant from the start of the first vector to the tip of the last.
Subtracting a vector
- Subtracting a vector means adding its negative, A − B = A + (−B).
Components
- Fx = F cos θ and Fy = F sin θ.
Perpendicular vectors
- R = √(A2 + B2) and tan θ = B ÷ A.
Components along the same line are added algebraically
- Components along the same line are added algebraically then Pythagoras and tangent give the resultant magnitude and direction.
Section 9 of 10Key terms
| Term | Meaning |
|---|---|
| SI base quantity | One of the independent quantities from which all others are derived. |
| Derived unit | A unit formed by multiplying or dividing SI base units. |
| Homogeneous equation | An equation with the same base units in every term. |
| Systematic error | An error that shifts all readings by the same amount or in the same direction. |
| Random error | An error that scatters readings unpredictably about the true value. |
| Absolute uncertainty | The range ±Δx in the same unit as the measurement. |
| Percentage uncertainty | The absolute uncertainty divided by the value, times 100%. |
| Resolving a vector | Splitting a vector into two perpendicular components. |
Section 10 of 10Exam technique
1
Using the wrong prefix power of ten, such as treating milli as 10-6.
2
Treating the gram as the base unit of mass — it is the kilogram.
3
Adding absolute uncertainties when multiplying — add percentage uncertainties.
4
Assuming a homogeneous equation must be correct.