Foundations
of Physics

Who knew that Napoleon Bonepart would have such a big impact on science? The metric system was born out of the French Revolution, but would take more than 100 years to be widely adopted, and America, Liberia and Myanmar are still holding on to the awkward imperial system of units. Even though the UK officially transitioned to the metric system in 1965, we still use a hybrid system of units – ultra awkward!

The appeal of the metric system is its simplicity – there are only 7 base units to know, and it’s quite fun to explore the history of how they’ve been defined. There was a large overhaul agreed in 2019 with the kilogram no longer being defined by a physical object.  But we’re probably not settled yet, a new definition of the second could be announced in 2030!

We can use prefixes in base 10 or standard form to cover the smallest and largest amounts of these quantities.  At A-level you’ll need to know…

• The 7 base units: metre, ampere, candela, mole, kelvin, second, kilogram
• Common prefixes: Peta, Tera, Giga, Mega, kilo, deci, centi, milli, micro, nano, pico, femto

 There are many other quantities, which all have a named unit associated with it – almost always in honour of a relevant scientist: Isaac Newton, James Watt, James Prescot Joule, Georg Ohm, Alessandro Volta, Nikola Tesla, Michael Faraday, Blaise Pascal, Anders Celcius, Charles-Augustin de Coulomb, Henri Bequerel, Heinrich Hertz etc. How many more can you name?

These examples are all also SI units, but we can break them down and build them up from a combination of the 7 fundamental base SI units in the previous section. Most of them are some combination of metres, seconds and kilograms, and sometimes the amp. 

At A-level you’ll be expected to be able to…

• How to express other SI quantities in terms of base units, e.g. N = kg m s^-2
• Using dimensional analysis to check the homogenity of equations
• Convert between units, e.g.  J to eV and kWh, m/s to mph etc.

Any physical quantity can be put into one of two baskets – they all have a magnitude (or size), but some of them also carry information about direction. These are things we can usually represent with an arrow – e.g. force, velocity, acceleration, momentum and fields.

There are some quantities which jump between baskets depending on the application, such as current and pressure, which are usually considered scalar quantities, but not when applying Flemings Left / Right Hand rules or cutting cheese with a knife etc.

At A-level you’ll be expected to be able to…

• State the definition of vector and scalar quantities
• Recall whether specific quantities are vectors or scalars
• Understand that only like quantities can be added or subtracted
• Appreciate that two vectors multiplied together might result in a scalar or a vector

You’ll find plenty of situations where multiple forces are acting on an object that may or may not be in equilibrium. Finding out whether there is a resultant force will dictate how/if the object will accelerate and its subsequent motion. These forces will usually act in a plane, so you’ll need to get used to using the key principles of trigonometry – Pythagoras’ Theorem and SOH-CAH-TOA. It could be helpful to also learn the sin and cosine rules, but I don’t think that’s actually necessary.

In reality forces could act in three dimensions and it’s helpful to know how to deal with 3D vectors – more so in Maths than A-level Physics. The rules of vector addition/subtraction can be applied to many other contexts, such as working out relative velocities or momentum in collisions/explosions etc. 

At A-level you’ll be expected to be able to…

• Add or subtract vectors in 2D by using scale drawings
• Add or subtract vectors in 2D by using trigonometry
• Draw vector triangles (or quadrilatals etc) for a system of forces on objects in equilibrium
• Find the resultant force vector for objects undergoing acceleration

Breaking down (resultant) vectors into perpendicular components will be vital when looking at projectile motion and looking at objects travelling along slopes and ramps. If you don’t want to remember the sine or cosine rules, it will also allow you to add/subtract non-perpendicular/parallel vectors using basic trigonometry.

Tip: Always draw a large diagram and label the components clearly. If you’re going to use basic trigonometry, I expect to see a right-angled triangle in your diagram. 

At A-level you’ll be expected to be able to…

• Resolve 2D vectors into perpendicular (e.g. horizontal and vertical) components
• Multiply parallel components together (dot product) to form a scalar (e.g. work done)
• Multiply perpendicular components together (cross product) to form a vector (e.g. the motor effect)

Practice makes perfect, so they say, and indeed you will get plenty of practice with vectors in both Maths and Physics. In Biology a vector is something entirely different!

• Projectile motion (resolving into independent x and y components to apply SUVAT equations)
• Dynamics problems with objects likely accelerating on inclined planes
• Kinematics problems with objects in linear and rotational equilibrium
• Superposition of waves to form interference patterns or stationary waves
• Forces felt by (moving) charged particles in electric and/or magnetic fields –  Y13
• Objects undergoing simple harmonic and/or circular motion – Y13