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
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
| Term | Meaning |
|---|---|
| Resultant | Single vector with the combined effect of the vectors. |
| Component | Part of a vector in one direction. |
| Pythagoras' theorem | FR² = F1² + F2² for perpendicular vectors. |
| Scale drawing | Accurate drawing with a chosen scale. |
| Tangent function | tan θ = opposite ÷ adjacent. |
| Vector diagram | Arrow 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.
Marked practiceQuizzes for this lesson
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