area metre-squared (m2)

density kilogram/metre-cubed (kg/m3)

distance metre (m) 

extension metre (m)

force  Newton (N)

gravitational field strength  Newton/kilogram (N/kg)

height  metre (m)

mass  kilogram (kg)

moment  Newton metre (Nm)

pressure  Pascal (Pa)

spring constant  Newton/metre (N/m)

weight  Newton (N)

work done Joule (J)

acceleration metre/second-squared (m/s2)

momentum  kilogram metre / second (kgm/s)

speed  metre/second (m/s)

velocity metre/second (m/s)

time  second (s)

Scalar quantities have magnitude only. Distance, speed and mass are scalar.

Vector quantities have magnitude and an associated direction. Displacement, velocity, force and acceleration are vector.

A vector quantity may be represented by an arrow. The length of the arrow represents the magnitude, and the direction of the arrow the direction of the vector quantity.

both have magnitude; only a vector has direction

A force is a push or pull that acts on an object due to the interaction with another object. All forces between objects are either:

  • contact forces – the objects are physically touching, e.g.  friction, air resistance, tension and normal contact force
  • non-contact forces – the objects are physically separated, e.g. gravitational force, electrostatic force and magnetic force.

Force is a vector quantity.

When two objects touch, there is a normal contact force between them, perpendicular to the surface where they touch.

Normal Contact Force

Weight is the force acting on an object due to gravity. The force of gravity close to the Earth is due to the gravitational field around the Earth.

The weight of an object depends on the gravitational field strength at the point where the object is.

The weight of an object can be calculated using the equation:

weight = mass × gravitational field strength

weight = mass × gravitational field strength

weight = 45 x 9.8

The weight of the gymnast is 441 Newtons

weight = mass × gravitational field strength

6.4 = mass x 9.8

mass = 6.4 / 9.8

The mass is 0.65 kg

The weight of an object may be considered to act at a single point referred to as the object’s ‘centre of mass’.

Weight is measured using a calibrated spring-balance (a newtonmeter).

The weight of an object and the mass of an object are directly proportional.

Directly Proportional

Directly Proportional Relationship

A directly proportional relationship is a straight line through the origin

The gradient is constant

The independent variable changes by the same value for each increment in the dependent variable

Inversely Proportional

Inversely Proportional Relationship

To show a graph is an inversely proportional relationship, at any point on the curve:

independent variable x dependent variable = a constant

Resultant Forces

A number of forces acting on an object may be replaced by a single force that has the same effect as all the original forces acting together. This single force is called the resultant force.

The resultant force is the sum of all the individual forces acting on an object

learn this definition
Zero Resultant Force
Non-zero Resultant Force

Names & Directions of Forces

Forces on a Plane
Forces on a Skier
Forces on a Lamp

Resolving Forces

A single force can be resolved into two components acting at right angles to each other. The two component forces together have the same effect as the single force.

Resolving Forces

Adding Forces

When more than one force is acting we can find the resultant force using a scale diagram. Draw the forces with a ruler and a protractor.

Parallelogram of Forces to find the Resultant Force

Doing Work With Forces

When a force causes an object to move through a distance work is done on the object. So a force does work on an object when the force causes a displacement of the object.

The work done by a force on an object can be calculated using the equation:

work done = force × distance moved along the line of action of the force

work done = force × distance moved along the line of action of the force

work done = 140 x 24

The work done is 3360 Joules

work done = force × distance moved along the line of action of the force

3430000 = force x 14

force = 3430000 / 14

The force is 245000 Newtons

One joule of work is done when a force of one newton causes a displacement of one metre. 1 joule = 1 newton-metre

Work done against the frictional forces acting on an object causes a rise in the temperature of the object.

The kinetic energy store of the bike will decrease

The thermal energy store of the brakes will increase