Tools and Inquiry — IB Physics skills
T.3.4 Scale Diagrams — IB Physics HL Revision Notes & Topical Questions
5 min read 8 parts Lesson 9 of 22 1 quiz
Lesson summary
T.3.4 Scale Diagrams — IB PHYSICS SL notes: Combine or resolve vectors by accurate scale drawing and convert measurements back using the scale.Calculation is used when the vectors are perpendicular.Scale drawing is used when the vectors are not perpendicular.Scale diagram questio…
- Scale diagram questions usually have vector triangles with no right angle
- Choose a scale that fits the page but is large enough for accuracy
- Only limited lengths can be measured with a ruler
- Draw lines to 1 mm and angles to 1°
- The answer is limited by the precision of ruler and protractor
- Check by calculation when possible
Part 1 of 6When to use a scale diagram
When to use a scale diagram
Calculation is used when the vectors are perpendicular.
Scale drawing is used when the vectors are not perpendicular.
Scale diagram questions usually have vector triangles with no right angle
- Scale diagram questions usually have vector triangles with no right angle a perpendicular case is quicker to calculate.
Part 2 of 6Choosing and stating the scale
Choosing and stating the scale
Choose a scale that fits the page but is large enough for accuracy
- Choose a scale that fits the page but is large enough for accuracy e.g. 1 cm = 1 km for 6 km and 10 km.
Only limited lengths can be measured with a ruler
- Only limited lengths can be measured with a ruler so a scale is needed.
The final answer is converted back to scenario units.
- With a scale of 1 cm = 2 km, a resultant of 5 cm is 10 km.
Part 3 of 6Drawing procedure
1
Choose a sensible scale and state it.
2
Draw the first vector accurately using a sharp pencil, ruler and protractor.
3
Link the next vector head to tail from the end of the first.
4
Draw the resultant using the triangle or parallelogram method.
5
Measure the length of the resultant with a ruler, accurate to 1 mm.
6
Measure the angle of the resultant with a protractor — from North if it is a bearing.
7
Convert the length using the scale and state magnitude and direction.
Part 4 of 6Accuracy of scale drawings
1Draw lines to 1 mm and angles to 1°
- Draw lines to 1 mm and angles to 1° a sharp pencil gives thin lines.
2
Larger drawings reduce the percentage uncertainty in measurements.
3The answer is limited by the precision of ruler and protractor
- The answer is limited by the precision of ruler and protractor quote it to a sensible number of figures.
4Check by calculation when possible
- Check by calculation when possible e.g. 6 km east and 10 km north gives about 11.7 km at 59° to the horizontal.
Part 5 of 6Direction and bearings
Direction and bearings
Bearings are measured clockwise from North.
Always state the reference
- Always state the reference angle from the horizontal, from the x-axis or from North.
Direction must accompany the magnitude
- Direction must accompany the magnitude the resultant is a vector.
Part 6 of 6More from the specification
1Vector scale diagrams for speed and power
- Vector scale diagrams for speed and power drawing vector triangles to scale enables geometric determination of resultant vehicle speed and engine power.
2Scale Diagrams and Vector Addition
- Vector quantities such as force and displacement are added by drawing scale diagrams tip-to-tail to determine resultant magnitude and direction.
3Linearizing Non-Linear Relationships
- Transforming physical equations (e.g. y = a xⁿ) using logarithms produces a straight line graph whose gradient and intercept yield physical constants.
4Graphical Determination of Rates of Change
- On kinematics graphs, the gradient of a distance-time curve represents instantaneous velocity,
- while the gradient of velocity-time represents acceleration.
5Significant Figures in Scientific Calculations
- Calculated quantities must be expressed to an appropriate number of significant figures consistent with the precision of experimental measurements.
6Absolute uncertainty
- The range ±Δx in the same unit as the measurement.
7Percentage error
- Difference from the accepted value as a percentage of it.
8Derived unit
- A unit formed by multiplying or dividing SI base units.
9Percentage difference
- Difference divided by accepted value × 100
10Gradient
- Slope of a graph line.
11Distance
- Total length of path travelled, a scalar.
12Variable
- A factor that can change in an investigation.
13Constant
- Not changing.
14Displacement
- Change in position.
15Proportional
- Changing by the same factor as another quantity.
16Scalar
- Quantity with magnitude only.
17Significant figures
- Digits carrying meaningful information in a number.
18a
− ω2x
What the symbols mean: a = acceleration (m s−2) · ω = angular frequency (rad s−1) · x = displacement from equilibrium (m); the minus sign means a always points back to the centre
Key terms
| Term | Meaning |
|---|---|
| Scale drawing | Accurate drawing in which lengths represent vector magnitudes. |
| Scale | Ratio linking drawn length to real quantity, e.g. 1 cm = 1 km. |
| Resultant | Single vector equivalent to the combination. |
| Bearing | Direction measured clockwise from North. |
| Protractor | Instrument for measuring angles. |
| Head-to-tail | Linking the start of one vector to the end of the previous. |
Avoid these mistakes
1
Drawing without stating the scale or forgetting to convert the measured length back.
2
Choosing a scale so small that the drawing is inaccurate.
3
Measuring the angle from the wrong reference line.
4
Linking vectors head to head instead of head to tail.
5
Giving only the magnitude of the resultant and no direction.
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