PHY C1: Physical Quantities & Units

Here’s a quick rundown of what we’ll be going through:

  • Physical Quantities
    • Reasonable Estimates of Quantities
  • SI Units & Base Units
    • Derived Units
    • Homogeneity of Equations
    • Standard Form
    • Prefixes
    • Labelling Graph Axes & Table Columns

Here we go!

What is a Physical Quantity?
A feature of something that can be measured.
A physical quantity consists of a MAGNITUDE (a number) & a UNIT (to show what quantity is measured).
Physical quantities include both BASE & DERIVED quantities.
Examples: velocity, energy, force, potential difference, charge, magnetic flux density, etc.

What is a Unit?
A unit is a definite magnitude of a physical quantity.
Examples: metres per second (m/s), Joules, Newtons (N), Coulomb (C), Tesla (T)

What is a Reasonable Estimate?
An estimated quantity associated with a system/device, within an acceptable range of values. In A-Levels, we need to have enough logical thinking to estimate the quantities of everyday situations/systems/objects.

Some examples are:
(I’ll update this later)

What is a Base Quantity?
A type of FUNDAMENTAL physical quantities that are NOT defined in terms of other physical quantities.
All other physical quantities are DERIVED from these base quantities.

What is an SI Unit?
The standardised Base UNITS used to measure Base Quantities that are agreed upon internationally to be used in science.

There are 7 official base SI units, which are:
Image result for Ampere

Extra Info:
Q: Why is Electric Current, Ampere (A) a Base Unit instead of Electric Charge, Coulomb (C)?

Extra Info:
What does ‘SI’ stand for?

What is Derived Quantity?
A physical quantity which is made up from a combination of the base (SI) quantities.
Examples of Derived Quantities: charge (Q), force (F), velocity (v)
Examples of Derived Units: 
Coulomb (C), Newton (N), metres per second (ms^-1)

What is a Homogenous Equation?
An equation that, when its units are broken up into their base units, is the SAME or BALANCED on both sides.

To check whether an equation is homogenous, break up its units into their base units, & compare both sides.

An equation is only CORRECT if it is HOMOGENOUS.
(However, a homogenous equation is NOT always correct – you still need to take constants into account: Read this discussion.)

Constants which have NO UNIT can be ignored when checking homogeneity, since you are only checking the UNITs and NOT their MAGNITUDE.

Examples of questions:

  1. Check whether equations are homogenous
  2. Find the base units of a derived unit
  3. Find the units of an unknown in a given equation
  4. Show that constants have no unit

What is Standard Form?
A method to write very large or very small units that avoids writing unnecessary zeros or decimal points.
For example, writing this: 0.0016
as this: 1.6 x 10⁻³
The rules are:
1. The numerical value must be a single digit
2. Any following digits must be after the decimal point
3. The significant digits are then multiplied by a power of 10

What are Prefixes?
An addition to the front of a unit of measurement to alter its magnitude (by powers of 10).
Prefixes are useful when dealing with measurements that would be too large or too small to deal with base units.
For example, adding centi- in front of a metre means it is a hundredth of a metre (a centimetre).

Here’s a list of Prefixes (in A-Levels, you only use Tera to Pico):
Image result for list of prefixes physics

What are the conventions we use in Physics regarding Units & Quantities?

  • Quantities are italicised (example: t)
  • Units are upright/romanised (example: s)

How do you label Table Column Headers?
For example:
Even though you might be used to it, do NOT write t(s).

If you need to LOG a quantity for whatever reason, write the header as:
lg (Quantity/Unit)

For example, when you log velocity, the header should be:
lg (v/km h⁻¹)

How do you label Graph Axes?
Graph axes use the same conventions as table headers.

⇒ Next in Physics: Scalars & Vectors

One thought on “PHY C1: Physical Quantities & Units

  1. New info! In physics, rounding has a special rule:
    when the last digit is a 5, round the number to the nearest even number.

    For example, in rounding to the nearest whole number:
    2.5 –> 2
    3.5 –> 4


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