Section 1 of 5Scalar or Vector?
Every physical quantity is either described by its size alone or by its size and direction.
Scalar
- A quantity with magnitude only, so a size and a unit give a complete description, as with mass, energy or speed.
Vector
- A quantity with both magnitude and direction, so a value alone is not enough, as with velocity, weight or force.
Magnitude
- The size or amount of a quantity, ignoring its direction, shown by the length of a vector arrow.
| Quantity | Type | Reason |
|---|---|---|
| Mass | Scalar | Size of matter only, no direction |
| Weight | Vector | A force that points towards the centre of the Earth |
| Speed | Scalar | How fast, with no direction |
| Velocity | Vector | Speed in a stated direction |
Section 2 of 5Common Scalar and Vector Pairs
Common Scalar and Vector Pairs
Distance
- A scalarthe total length of path travelled, with no direction attached to it.
Displacement
- A vectorthe straight-line change in position from start to finish, for example 100 km north.
Speed
- A scalarhow fast an object moves, regardless of the direction it is moving in.
Velocity
- A vectorspeed in a stated direction, for example 60 km/h due west.
Section 3 of 5Drawing Vectors
A vector diagram is a scale drawing, so the arrows must be proportional to the values they represent.
1
Choose a scale that lets the largest vector fit on the page, and use the same scale for every arrow.
2
Draw each arrow with a length proportional to its magnitude, so an arrow twice as long shows twice the magnitude.
3
Point each arrowhead in the direction of the quantity, measuring any angle from the horizontal or vertical with a protractor.
4
Label every vector with its name and value, so a reader can see both its magnitude and its direction.
Section 4 of 5Worked Example
Question
- A car travels 60 km in one hour, always in a straight line due west.
- State which of the values are scalars and which is a vector, and give the velocity of the car.
- Speed is the rate of distance covered, so it has magnitude only and is a scalar: 60 km/h.
- Velocity is speed with a direction, so it is a vector.
- Add the direction to the speed to give the velocity.
Answer
- Speed 60 km/h is a scalar;
- velocity is 60 km/h due west, a vector.
Section 5 of 5Exam Checklist & Tips
1.1.1 – Key Points for the Exam
- Scalar A quantity described completely by its magnitude and unit.
- Vector A quantity described by both its magnitude and its direction.
- Magnitude The size of a quantity, without regard to direction.
- Displacement The straight-line change in position of an object, with direction.
- Velocity The speed of an object in a given direction.
Common Mistakes
- Calling distance and displacement the same thing; distance is a scalar while displacement is a vector.
- Giving a velocity without a direction, which turns it into a speed.
- Thinking weight is a scalar because it is measured with a single number;
- weight is a force, so it is a vector.
- Drawing a longer arrow for a larger angle instead of a larger magnitude.