A mass of 2 kg is just a number with a unit. A force of 2 N pushing east is something more: it has a direction, and pointing it the other way changes the physics entirely. That difference splits every physical quantity into two families.
A scalar has magnitude (size) only. A vector has both magnitude and direction. Speed, distance, mass, time and energy are scalars; velocity, displacement, acceleration, force, weight and momentum are vectors.
A vector is drawn as an arrow: its length shows the magnitude and the way it points shows the direction. Watch the orbit below. The speed (a scalar) never changes, but because the direction is constantly shifting, the velocity (a vector) is constantly changing.
Four quick checks on the definitions and on what the orbit demonstrates. Each correct answer earns XP and lights this skill on your star map.
As the object moves around the circle at constant speed, its velocity...
A scalar quantity has...
Which of these is a vector quantity?
The orbit keeps a fixed speed but a changing velocity because...
| Scalars (magnitude only) | Vectors (magnitude and direction) | |
|---|---|---|
| Examples | distance, speed, time, mass, energy, temperature | displacement, velocity, acceleration, force, weight, momentum, gravitational field strength |
Notice the pairs that are easy to confuse: distance (scalar) versus displacement (vector), and speed (scalar) versus velocity (vector). The vector version of each carries a direction; the scalar version does not.
Because a vector has direction, the sign matters. A velocity of +5 m/s and one of −5 m/s have the same speed but opposite directions, and treating them as the same value is exactly the error that loses marks in momentum and force questions. Always decide which direction is positive before you start.
Classify each of the following as a scalar or a vector: (i) the mass of a trolley, (ii) the velocity of a car, (iii) the distance walked, (iv) the weight of a book.
Unlocks once the four checks above are done. Worth more XP, written in the style of Paper 2.
Which list contains only vector quantities?
A car moves at +8 m/s, then travels at the same speed the opposite way, written as −8 m/s. These two values describe...
Distance is a scalar. Its vector counterpart, which also carries a direction, is...
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