Scalars and Vectors
Section: Motion, Forces & Energy | Syllabus: Cambridge IGCSE Physics (0625)
Scalar and Vector Quantities
Extended Only
- A scalar quantity has magnitude (size) only
- A vector quantity has both magnitude and direction
- Scalars (syllabus list):
- distance, speed, time, mass, energy, temperature
- Vectors (syllabus list):
- force, weight, velocity, acceleration, momentum, electric field strength, gravitational field strength
| Scalar Quantities | Vector Quantities |
|---|---|
| Distance | Displacement |
| Speed | Velocity |
| Mass | Weight |
| Time | Force |
| Energy | Acceleration |
| Temperature | Momentum |
| - | Gravitational field strength |
| - | Electric field strength |
- Don't confuse speed (scalar) with velocity (vector) - velocity includes direction, speed doesn't
Representing Vectors
Extended Only
- Vectors are represented by arrows, showing both magnitude and direction
- the length of the arrow represents the magnitude
- the direction the arrow points represents the direction of the vector
An arrow's length shows magnitude, and its direction shows the vector's direction
Finding the Resultant of Two Perpendicular Vectors
Extended Only
- You need to be able to find the resultant of two vectors at right angles to each other, limited to forces or velocities only
- Two methods are acceptable: graphically (scale drawing) or by calculation
Method 1: Graphical (Scale Drawing)
- Draw the two vectors to scale, placed head to tail
- Draw the resultant from the tail of the first vector to the head of the second
- Measure its length and direction with a ruler and protractor
Drawing the vectors head to tail and measuring the resultant with a ruler and protractor
Method 2: By Calculation (Pythagoras' Theorem)
- For two vectors at right angles, the resultant is the hypotenuse of a right-angled triangle
- Magnitude:
- R = √(A^2 + B^2)
- Direction:
- θ = tan^-1((B/A))
- the angle from vector A towards vector B
Always draw the right-angled triangle first, then apply Pythagoras and trigonometry
Worked Example: Finding a Resultant Force
Museli has two perpendicular forces acting on a point: 3 N and 4 N, and wants to find the resultant force.
- Step 1: find the magnitude. R = √(3^2 + 4^2) = √(25) = 5 N
- Step 2: find the direction. θ = tan^-1((4/3)) = 53.1°
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