Physical quantities are more than just numbers

Every physical quantity consists of two essential components:

1. A numerical value
2. A unit of measurement

When measuring or calculating any quantity, it's crucial to always include the appropriate unit.

The foundation: Base quantities and SI units

The Système International (SI) establishes seven fundamental base quantities. All other quantities, known as derived quantities, can be expressed in terms of these base quantities.

Derived quantities and their units

Derived quantities are those that can be expressed in terms of base quantities. Their units, called derived units, are combinations of base units.

For example:

The Coulomb (C) is a derived quantity. We can use the equation Q = I x t, to find the S.I. base units.

• 1 C is equivalent to 1 A s.

Worked example - Understanding the Newton

Show that 1 Newton is equivalent to 1 kilogram metre per second squared (kg m s^-2)

Step 1: Identify the base units

• mass: kilogram (kg)
• acceleration: metre per second squared (m s^-2^)

Step 2: Substitute units into the equation

Force = mass x acceleration

Units of force = kg x m s^-2 = kg m s^-2

Worked example - Deriving the unit for speed

Demonstrate that the S.I derived unit for speed is m/s.

Step 1: Identify the base units

• Distance: metre (m)
• Time: second (s) Step 2: Apply the speed formula with units

Speed = distance ÷ time

Units of speed = m ÷ s = m/s

Scaling units with prefixes

To accommodate the vast range of quantities in physics, we use prefixes to scale units. This approach avoids the need for constant use of standard form.