Tools and Inquiry — IB Physics skills
T.3.2 Scalar and Vector Quantities — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 7 of 22 1 quiz
Lesson summary
T.3.2 Scalar and Vector Quantities — IB PHYSICS SL notes: Distinguish scalars from vectors and use direction as well as magnitude for displacement, velocity, acceleration and force.Scalar = a quantity with magnitude only — e.g.
- A scalar is a number and a unit
- Vectors add by geometry
- A scalar times a vector is a vector
- Components are drawn with dotted lines and subscripts
- A component along an axis is a signed number
- Energy cannot be directed
Part 1 of 7Scalars and vectors
1Scalar
Scalar a quantity with magnitude only — e.g. mass.
2Vector
Vector a quantity with both magnitude and direction — e.g. weight, because it is a force.
3A scalar is a number and a unit
- A scalar is a number and a unit a vector must also state a direction.
4Vectors add by geometry
- Vectors add by geometry not by simple arithmetic.
Part 2 of 7Distance and displacement
Distance
Distance how far an object has travelled regardless of direction — the total path length, a scalar.
Displacement
Displacement the straight-line distance and direction from start to finish — a vector.
A student travelling to school covers a distance along all the twists of the roads.
- Their displacement is the straight line from home to school.
A runner completing one lap of a 400 m track has distance 400 m but displacement zero.
Part 3 of 7Speed, velocity and acceleration
Speed
Speed distance per unit time — a scalar that gives how fast but not which way.
Velocity
Velocity displacement per unit time — a vector with magnitude and direction.
An object can have constant speed but changing velocity if its direction changes.
Acceleration a
Δv / Δt is a vector.
- A car at constant speed round a bend is accelerating, because the direction of velocity changes.
Average speed over a path is not the magnitude of the average velocity.
Part 4 of 7Common scalars and vectors
| Scalars | Vectors |
|---|---|
| Distance | Displacement |
| Speed | Velocity |
| Mass | Acceleration |
| Time | Force |
| Energy | Momentum |
| Volume, density | Electric field |
| Pressure | Gravitational field strength |
| Electric charge, temperature | Weight |
- A scalar times a vector is a vector
- F = ma and p = mv.
Part 5 of 7Representing vectors
Representing vectors
A vector is drawn as an arrow.
- The arrowhead shows the direction.
- The length shows the magnitude.
Components are drawn with dotted lines and subscripts
- Fx is horizontal and Fy is vertical.
A component along an axis is a signed number
- A component along an axis is a signed number it is used like a scalar in calculations, but it belongs to a vector.
Part 6 of 7Telling scalars from vectors
1
Ask whether direction matters when two of them are added.
- Two 5 N forces give anything between 0 N and 10 N, so force is a vector.
- Two 5 kg masses always give 10 kg, so mass is a scalar.
2
A minus sign does not make a quantity a vector.
- Work done and gravitational potential energy are scalars that can be negative.
3Energy cannot be directed
- Energy cannot be directed but displacement can be negative, showing direction.
4
Does it point somewhere? A push, a pull, a change of position or a field acting on a charge are vectors.
Part 7 of 7More from the specification
1Scalar definition of power
- Scalar definition of power rate of energy transfer per unit time is a scalar quantity, defining electrical or mechanical power.
2Negative sign
- Negative sign a minus sign only shows direction along a chosen axis;
- it does not by itself make a quantity a vector.
3Negative sign
- Negative sign a minus sign only shows direction along a chosen axis;
- it does not by itself make a quantity a vector.
4Percentage error
- Difference from the accepted value as a percentage of it.
5Derived unit
- A unit formed by multiplying or dividing SI base units.
6Percentage difference
- Difference divided by accepted value × 100
7Scale drawing
- Accurate drawing with a chosen scale.
8Parallelogram method
- Vector addition using a parallelogram of vectors.
9Uncertainty
- An estimate of the range in which the true value is expected to lie.
10Gradient
- Slope of a graph line.
11Resultant
- Vector sum of two or more vectors.
12Variable
- A factor that can change in an investigation.
13Proportional
- Changing by the same factor as another quantity.
14Significant figures
- Digits carrying meaningful information in a number.
15Resultant vector
- Single vector equivalent to a combination of vectors.
16Percentage uncertainty
- The absolute uncertainty divided by the value, times 100%.
17a
− 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
18Negative sign
- Negative sign a minus sign only shows direction along a chosen axis;
- it does not by itself make a quantity a vector.
Key terms
| Term | Meaning |
|---|---|
| Scalar | Quantity with magnitude only. |
| Vector | Quantity with magnitude and direction. |
| Distance | Total length of the path travelled; a scalar. |
| Displacement | Straight-line distance and direction from start to finish; a vector. |
| Speed | Distance travelled per unit time; a scalar. |
| Velocity | Displacement per unit time; a vector. |
| Component | Part of a vector along a chosen axis. |
Avoid these mistakes
1
Using distance when displacement is required — direction matters for a vector.
2
Thinking a negative number means a quantity is a vector — scalars such as work can be negative.
3
Saying constant speed means no acceleration — a changing direction is an acceleration.
4
Adding vectors arithmetically without considering direction.
5
Equating average speed with the magnitude of average velocity for a curved path.
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