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1.1.3Motion, Forces and Energy

Calculating with Vectors — Cambridge IGCSE Physics 0625 Revision Notes & Topical Questions

5 min read 8 parts Lesson 7 of 91 1 quiz

📚 Cambridge IGCSE Physics 0625 Hub / Topical Revision
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Lesson summary

1.1.3 Calculating with Vectors — IGCSE Physics Notes — IGCSE PHYSICS notes: Find the resultant of two perpendicular vectors by scale drawing and by calculation.Arrow — a vector is drawn as an arrowLength — it represents the magnitude, to a chosen scaleDirection — the arrowhead sh…

  • Resultant vector
  • Right angles
  • Components
  • Choose a scale that fits the page, such as 1 cm
  • Pythagoras' theorem
  • Tangent function

Part 1 of 6Vector diagrams

Arrow
  • Arrow a vector is drawn as an arrow
Length
  • Length it represents the magnitude, to a chosen scale
Direction
  • Direction the arrowhead shows the direction
Scale
  • Scale a 4 N force is drawn twice as long as a 2 N force

Part 2 of 6Resultant and components

Resultant and components
Resultant vector
  • Resultant vector a single vector with the combined effect of two vectors
Right angles
  • Right angles vectors at right angles combine into one resultant
Components
  • Components drawn with a dotted line, for example FH is the horizontal component and FV is the vertical component

Part 3 of 6Combining vectors by scale drawing

1Choose a scale that fits the page, such as 1 cm
10 m/s or 1 cm = 1 N.
2
Draw the two vectors at right angles to each other.
3
Complete the rectangle.
4
Draw the resultant diagonally from the origin.
5
Measure the length of the resultant and use the scale to find the magnitude.
6
Use a protractor to measure its angle.

Part 4 of 6Combining vectors by calculation

Diagram
  • Diagram a sketch is enough if the resultant and the components are labelled
Magnitude
  • Pythagoras gives FR² = F1² + F2²
Angle
  • Angle tan θ = opposite ÷ adjacent, so θ = tan⁻¹(F1 ÷ F2)
Result
  • Result state both the magnitude and the direction
Limit
  • Limit in this course the resultant of two vectors is for forces and velocities only

Part 5 of 6Calculation example

Data
  • 60 N to the right and 100 N upwards
Magnitude
  • F = √(60² + 100²) = √13 600 = 117 N
Angle
  • θ = tan⁻¹(100 ÷ 60) = 59° from the horizontal
Answer
  • 117 N at 59° from the horizontal

Part 6 of 6More from the specification

1Scalar quantities
  • Scalar quantities have magnitude only, such as distance, speed, volume and energy
2Vector quantities
  • Vector quantities have magnitude and direction, such as displacement, velocity and force
3Vector addition
  • Vector addition combine vectors by scale drawing or resolving into perpendicular components and using Pythagoras
4Measurement
  • Measurement quantities have units, and the distance taken by an object differs from its displacement
5Displacement
  • Change in position.
6Reference marker
  • Fixed mark showing the equilibrium position of an oscillation.
7Scalar
  • Quantity with magnitude only.
8Distance
  • Total length of path travelled, a scalar.
9Volume
  • The amount of space an object occupies.
10Bearing
  • Direction measured clockwise from North.

Key terms

TermMeaning
ResultantSingle vector with the combined effect of the vectors.
ComponentPart of a vector in one direction.
Pythagoras' theoremFR² = F1² + F2² for perpendicular vectors.
Scale drawingAccurate drawing with a chosen scale.
Tangent functiontan θ = opposite ÷ adjacent.
Vector diagramArrow diagram of vectors.

Avoid these mistakes

1
Adding the magnitudes of perpendicular vectors — use Pythagoras for the resultant.
2
Giving a resultant without its direction — state magnitude and direction.
3
Forgetting the scale conversion in a scale drawing — convert the measured length with the scale.
4
Using the wrong ratio for the angle — tan θ = opposite ÷ adjacent.

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