### Calculus Proof of Centripetal Acceleration Magnitude

In basic circular motion in physics we are given the following equation for the centripetal acceleration on a body moving in circular motion: However how can this be proved? Well, acceleration is a vector- so what we need to know is it’s magnitude and direction. The second part of which is obvious, it’s in the […]

### A brief overview of ‘randomness’ and ‘noise’

What is pseudo-randomness? If you were asked to generate a number in your head in the bounds of 1 to 10, you may say that it’s a pretty easy task. You may even say that the probability of someone guessing your generated number is 1 in 10. However this is far from the case. People […]

### Proving the Volume of a Sphere (Cylindrical Co-ordinates feat. triple integrals)

We are always taught that the volume of a sphere is 4/3πr^3 at school. But how can this be proved? One of the ways is to use cylindrical co-ordinates and integrate over suitable ranges in each of this co-ordinate system’s dimensions. But before we can do this, what are cylindrical co-ordinates? Cylindrical co-ordinates is similar […]

### Cold Plasma Oscillations – Frequency Derivation

At low temperatures it is not a bad model to take a plasma as a collection of ions and electrons, with the ions always stationary, and the electrons oscillating, due to the force upon them due to the opposing charges of the electrons and ions. For this derivation we will assume that the ions ans […]

### Schwarzschild radius – Classical Derivation

If you want to derive the Schwarzschild radius for a given body, without mastering linear algebra and tensor mathematics – don’t fear. There is a classical method, that gets to the right answer. No need to delve into the Schwarzschild metric, when you have trusty old Newton. **Disclaimer- If you can always do this derivation the […]

### The Exponential Function – Why so useful?

An exponential function is a function where the input variable (usually written as x) is an exponent. Functions with constants in the exponent are also considered exponential functions. Then what is so amazing about these exponential functions? It all comes down to the rate of change of such a function (also known as the derivative […]

### Double Slit Interference, and Quantum Weirdness!

Young’s double slit experiment is one of the most well-known experiments in the history of physics. Showing that light behaves as a wave, which we later on found out wasn’t always the case, the experiment was originally carried out by Thomas Young in 1801. Young obviously had no ideas about the implications the experiment would […]

### Pauli’s Exclusion Principle ¬ Basic “Proof”

One very important concept and principle of quantum mechanics is the Pauli exclusion principle. Responsible for things such as different electron orbits, it can be observed in many places. The exclusion principle states that no two Fermions can occupy the same quantum state.  But what does this mean? This can be shown in terms of […]

### PlanckTime Forum: What you need to know!

We are super excited to announce the PlanckTime Forum! At the moment we have sections for most areas of physics (quantum mechanics, relativity…) and also sections for maths and computer science. We will be expanding the forum to cater for all “physicsy” and “mathsy” needs to create our awesome online community. You will need to […]

### Simple Time Dilation Derivation | Special Relativity

As I was interested I decided to derive the time dilation equation. My video if you’re interested in doing so yourself is linked here. To begin with I took 2 observers, one stationary and one moving. Both use a photon clock to measure the passage of time. It’s just two parallel plates, when a photon […]