Scalars, Vectors and Resultant Forces Notes
AQA GCSE Physics: Revision notes
Key facts
- A scalar has magnitude only; a vector has magnitude and direction.
- Contact forces need touching; non-contact forces act at a distance.
- The resultant force is the single force with the same effect as all the forces together.
- Balanced forces give zero resultant: no change in motion. Unbalanced forces cause acceleration.
- Higher tier: resolve a force into two perpendicular components, or combine forces with a scale vector diagram.
Scalars and vectors
A scalar has size only; a vector has size and direction, and is drawn as an arrow.
A scalar quantity has magnitude only. A vector quantity has magnitude and direction.
Vectors are drawn as arrows: the length shows the magnitude and the arrow points in the direction.
Speed is a scalar (10 m/s). Velocity is a vector (10 m/s north).
| Scalar | Vector | |
|---|---|---|
| Has | Magnitude only | Magnitude and direction |
| Examples | Distance, speed, mass, energy, time | Force, velocity, displacement, acceleration |
Scalar
- Has:
- Magnitude only
- Examples:
- Distance, speed, mass, energy, time
Vector
- Has:
- Magnitude and direction
- Examples:
- Force, velocity, displacement, acceleration
Which of these is a vector quantity?
Contact and non-contact forces
A force is a push or pull; contact forces need touching, non-contact forces act across a gap, and interacting objects exert a pair of forces.
A force is a push or pull that can change the motion, shape or direction of an object. It is a vector.
When two objects interact, each exerts a force on the other, and these forces act as a pair.
| Contact force | Non-contact force | |
|---|---|---|
| Acts when | Objects are touching | Objects are separated |
| Examples | Friction, air resistance, tension, normal contact force | Gravitational, electrostatic, magnetic force |
Contact force
- Acts when:
- Objects are touching
- Examples:
- Friction, air resistance, tension, normal contact force
Non-contact force
- Acts when:
- Objects are separated
- Examples:
- Gravitational, electrostatic, magnetic force
Which of these is a non-contact force?
Resultant force
Add forces in the same direction and subtract forces in opposite directions; zero resultant means balanced forces.
Several forces can be replaced by one resultant force with the same effect.
If the resultant is zero the forces are balanced and the motion does not change: the object stays still or keeps a constant velocity. If it is not zero, the forces are unbalanced and the object accelerates in the direction of the resultant.
A free body diagram shows all the forces on one object as arrows.
- Same directionadd
- Opposite directionssubtract
Worked example
A box is pulled right with a force of 15 N and left with a force of 6 N. Find the resultant force.
- 1
The forces act in opposite directions, so subtract: 15 − 6 = 9.
- 2
The resultant acts in the direction of the larger force, which is to the right.
The forces on a car are balanced. Which statement must be true?
Forces at an angle
Draw the forces to scale and complete the parallelogram to find the resultant; a force can be split into two perpendicular components.
Higher tier. A single force can be resolved into two components at right angles, for example the horizontal and vertical parts of a force pulling at an angle.
To combine two forces at an angle, draw them to scale from one point and complete the parallelogram. The diagonal is the resultant, and you measure its length and angle.
What is the resultant of a 3 N force and a 4 N force acting at right angles?
Try an exam question
A box is pulled to the right with a force of 15 N and to the left with a force of 6 N. Calculate the resultant force and state its direction. Describe the motion of an object when the forces on it are balanced.
[4 marks]
- [1]Resultant force = 15 − 6.
- [1]9 N to the right.
- [1]When the forces are balanced the resultant force is zero.
- [1]The object stays at rest or keeps moving at a constant velocity.
That's the notes covered.
Carry on to the next subtopic.