Scalar and vector quantities
I.
What is a Scalar Quantity?
A scalar quantity is a quantity that has magnitude only. Only having magnitude means that a
quantity only has a certain size but no direction. Examples of scalar quantities are time, speed
and mass.
II.
What Is a vector quantity?
Quantities that do have direction in addition to their magnitude are called vector quantities.
Vectors can be shown as arrows, their length and direction representing the magnitude and
direction, respectively. Examples of vectors are force, velocity or acceleration.
III.
Example in context
In an example of speed and velocity a car may be travelling at 30 miles per hour (its speed), but
this does not tell us anything about where the car is travelling. Speed is therefore a scalar
quantity. Adding a further piece of information for velocity, for example that the car is travelling
at 30 miles per hour north, now gives us information about the direction and makes velocity a
vector quantity.
IV.
Force
A force is always exerted on an object in a specific direction. The object might be pushed or
pulled for example. When drawing force diagrams, the force is always shown as an arrow
pointing in the direction in which the force is exerted, such as in the diagram in Figure 1.
Figure 1: A force diagram with two forces applied to an object,
shown as red and blue arrows.
When two vectors are added together, e.g. when two forces act on an object, the resulting
vector has to take both the magnitude and the direction into account. In the example in Figure 1,
the red arrow is twice as long as the blue arrow, so the resultant force would be calculated by
adding the lengths and directions of the red arrow and the blue arrow:
Resultant force = [length and direction of red arrow] + [length and direction of blue arrow].
In the above example, this would be:
Resultant force
= [length of red arrow] + [- length of red arrow]
Therefore
= + [ length of red arrow].
The direction of the resultant force would be in the direction that the red arrow is pointing. The
direction of the blue arrow was taken as minus the direction of the red arrow, because it is
acting in the opposite direction.
Questions
1. A vector quantity is ….
A. a quantity that has only magnitude and no direction.
B. a quantity that has both magnitude and direction.
C. a quantity that only has direction.
D. a quantity that has a volume.
2. A scalar quantity is ….
A. a quantity that has both magnitude and direction.
B. a measure of gravity outside the Solar System.
C. a quantity that has only magnitude and no direction.
D. a specific force that acts in the positive direction.
3. A vector quantity can be represented as an arrow. What does the length of the arrow
represent?
A. The magnitude of the quantity.
B. The direction of the quantity.
C. The three-dimensional properties of the quantity.
D. It does not represent anything, it is arbitrary.
4. Which one of these is a vector quantity?
A. Speed
B. Mass
C. Time
D. Acceleration
5. Which one of these is a scalar quantity?
A. Force
B. Velocity
C. Speed
D. Acceleration
6. Why is force a vector quantity?
A. Because it has both direction and magnitude.
B. Because it has magnitude but no direction.
C. Because it has direction and acceleration.
D. Because it is applied to an object.
7. Which one of these statements is true about displacement?
A. All of the below are true.
B. Displacement has both magnitude and direction.
C. Displacement is the distance travelled in astraight line.
D. Displacement is a vector quantity
8. Which statement about vector and scalar quantities is correct?
A. Time is a vector quantity as it both magnitude but no direction.
B. When vectors are added, both the direction and the magnitude have to be taken
into account.
C. Force is always exerted in one direction; therefore the magnitude of the force is
irrelevant.
D. Acceleration is a vector quantity because it is calculated by dividing speed by time.
9. Which one of these is a vector quantity?
A. 60 m / s
B. 20 N at 30°
C. 11 g
D. 5 o’clock
10. Which statement about energy is correct?
A. Energy is calculated using the following equation: energy = voltage / charge
B. Energy is a created by burning coal in coal-fired power stations.
C. Energy is often destroyed in experiments.
D. Energy is a scalar quantity.
Answers
1. B
2. C
3. A
4. D
5. C
6. A
7. A
8. B
9. B
10. D