Scalars, Vectors and Resultant ForcesAQA GCSE Physics: Revision notes
Section 1
What Is the Difference Between a Scalar and a Vector?
- A scalar quantity has magnitude (size) only, e.g. distance, speed, mass, energy, time.
- A vector quantity has both magnitude and direction, e.g. force, velocity, displacement, acceleration.
Vector quantities are often represented by arrows: the length of the arrow shows the magnitude and the direction the arrow points shows the direction of the quantity.
Speed (a scalar, e.g. '10 m/s') tells you only how fast something moves. Velocity (a vector, e.g. '10 m/s north') also tells you which way.
Section 2
What Is a Force, and How Do Contact and Non-Contact Forces Differ?
A force is a push or pull that can change the motion, shape or direction of an object. Forces are vector quantities.
- Contact forces act only when two objects are physically touching, e.g. friction, air resistance, tension, normal contact force.
- Non-contact forces act between objects that are physically separated, e.g. gravitational force, electrostatic force, magnetic force.
When two objects interact, each exerts a force on the other — these forces act as a pair.
Section 3
How Do You Find the Resultant of Forces Acting in a Straight Line?
When more than one force acts on an object, they can be replaced by a single resultant force that has the same overall effect.
- Forces acting in the same direction are added together.
- Forces acting in opposite directions are subtracted, and the resultant acts in the direction of the larger force.
- If the resultant force is zero, the forces are described as balanced and the object's motion does not change (it stays still or continues at a constant velocity).
- If the resultant force is not zero, the forces are unbalanced and the object accelerates in the direction of the resultant.
Free body diagrams show all the forces acting on a single object as arrows, which can be used to work out the resultant force.
A box is pulled right with 15 N and left with 6 N. The resultant force is 15 − 6 = 9 N to the right.
Balanced forces mean zero resultant force, not zero forces — an object can have several forces acting on it and still not accelerate.
Section 4
How Do You Resolve and Combine Forces at an Angle? (HT)
A single force can be resolved (split) into two component forces acting at right angles to each other — for example, splitting a force pulling at an angle into a horizontal and a vertical component.
Conversely, two forces acting at an angle to each other can be combined using a scale vector diagram: draw the two force arrows to scale, then draw the diagonal of the parallelogram they form to find the magnitude and direction of the resultant force.
For HT vector diagram questions, always draw arrows to a stated scale and measure the resultant's length and angle with a ruler and protractor.
Must Know
- Scalars have magnitude only (e.g. speed, mass); vectors have magnitude and direction (e.g. force, velocity).
- Vectors are represented by arrows: length shows magnitude, direction shows direction.
- Contact forces need touching objects (friction, tension); non-contact forces act at a distance (gravity, magnetism, electrostatic).
- The resultant force is the single force with the same effect as all forces combined; forces in a line are added or subtracted.
- Balanced forces (resultant = 0) cause no change in motion; unbalanced forces cause acceleration.
- (HT) A force can be resolved into two perpendicular components, and forces at an angle can be combined using a scale vector diagram.
That's the notes covered.
Carry on to the next subtopic.