1.2 - Scalar & Vector Quantities
Scalar and vector quantities
- A scalar quantity has magnitude (size) only.
- A vector quantity has both magnitude and direction.
| Definition | Examples | |
|---|---|---|
| Scalar | Magnitude only | distance, speed, mass, time, temperature, energy |
| Vector | Magnitude and direction | displacement, velocity, acceleration, force, momentum |
Speed vs velocity, distance vs displacement
- Speed tells you only how fast something is moving, so it's a scalar.
- Velocity tells you how fast and in which direction, so it's a vector.
- Distance is a scalar, but displacement (the straight-line distance and direction from start to finish) is a vector.
- Acceleration is a vector. Its matching scalar is the rate of change of speed, which has magnitude only.
Representing vectors with arrows
- A vector is drawn as an arrow.
- The length of the arrow shows the magnitude of the quantity.
- The direction of the arrow shows the quantity's direction.
- Two objects travelling at the same speed in opposite directions have arrows of the same length pointing opposite ways: the same speed, but different velocities.
Positive and negative directions
- When a vector acts along a line, one direction is chosen as positive and the opposite direction as negative.
- A velocity of 3 m/s in one direction is -3 m/s in the opposite direction (the speed is 3 m/s in both cases).
- A 10 N force in one direction is -10 N in the opposite direction.
Interaction pairs
Whenever two objects interact, they exert an interaction pair of forces on each other.
The two forces in an interaction pair:
- Are the same type of force
- Are equal in size
- Act in opposite directions
- Act on different objects
A hand pushing a wall and the wall pushing back are an interaction pair.
Examples of interaction pairs
- Contact force - A chair pushes down on the ground, and the ground pushes back up on the chair with an equal and opposite normal contact force.
- Non-contact force - The Sun pulls on the Earth, and the Earth pulls on the Sun with an equal and opposite gravitational force.
Why the forces don't cancel
- Because the two forces act on different objects, they do not cancel each other out.
- Cancelling only happens when forces act on the same object.
TermDefinition
Scalar quantityA quantity that has magnitude (size) only, with no direction.
Vector quantityA quantity that has both magnitude (size) and direction.
DisplacementThe straight-line distance from a starting point to a finishing point, together with its direction.
Interaction pairA pair of forces of the same type that are equal in size and opposite in direction, acting on two different interacting objects.