Scalars, vectors and resultant forces · GCSE Physics

Scalars and vectors

Scalar quantities have magnitude (size) only, for example distance, speed, mass, energy, time and temperature.
Vector quantities have magnitude and direction, for example displacement, velocity, acceleration, force and momentum.
A vector can be shown as an arrow: its length shows the magnitude and its direction shows the direction.

A force is a push or a pull that acts on an object because of its interaction with another object. Force is a vector.
Contact forces need the objects to touch: friction, air resistance, tension and normal contact force.
Non-contact forces act at a distance: gravitational, electrostatic and magnetic forces.

Weight is the force acting on an object due to gravity. It is measured in newtons (N).
W = m g: weight (N) = mass (kg) × gravitational field strength (N/kg). On Earth, g is about 9.8 N/kg (Edexcel and OCR papers use 10 N/kg).
Weight acts at a single point called the centre of mass. It can be measured with a newtonmeter (a calibrated spring balance).
Weight and mass are directly proportional, but mass is the same everywhere while weight depends on the gravitational field strength.

The resultant force is the single force that has the same effect as all the forces acting on an object together.
Forces in the same direction add; forces in opposite directions subtract.
If the resultant force is zero, the forces are balanced.
(Higher) A free body diagram shows all the forces on an object. A single force can be resolved into two components at right angles, and forces can be added using a scale drawing.

Scalar: A quantity with magnitude only, such as speed or mass.
Vector: A quantity with magnitude and direction, such as velocity or force.
Force: A push or pull on an object caused by an interaction with another object.
Contact force: A force that acts only when objects touch, such as friction.
Non-contact force: A force that acts at a distance, such as gravity.
Weight: The force of gravity on an object: W = mg.
Centre of mass: The point where the weight of an object can be taken to act.
Resultant force: The single force that has the same effect as all the forces on an object.
Newton: The unit of force (N).