 ## The Energy discipline is live!

A new discipline in the fundamentals of Energy is live! Momentum, impulse, force, acceleration etc. are all involved with causing motion. Energy on the other…

## Proof 37: Elastic potential energy

In a spring that is elongated/compressed the distance $\Delta L=L_\text{end}-L_\text{relaxed}$, an elastic force (due to Hooke’s law) $F_\text{elastic}=k\Delta L$ is pushing/pulling on the surroundings in…

## Proof 36: Gravitational potential energy

Small falling object due to weight A flower pot falls down from a window sill due to gravity. This i because gravity does work $W_g$…

## Proof 35: Kinetic energy

Linear version of kinetic energy A spaceship in outer space starts its rocket engines to propel itself forwards with a rocket force. That force does…

## Resource: Energies overview

Overview of typical energies that we encounter or hear about in everyday life. This list can be extended massively within various fields of science, such…

## NASA recording confirming Galileo

You’ve heard that everything falls equally fast, right? A counter-intuitive phenomenon. It’s not easy to see here on Earth with wind and air resistance interfering.…

## Launch of the Interaction discipline!

Our new discipline in Interaction is out today! If you want to know more about, why impacts, collisions and punches hit so hard, about action/reaction…

## Proof 34: Precession

Proof of the precession angular speed formula $\omega_\text{precession}=\frac{wr}{L_\text{spin}}$ is coming soon.

## Proof 33: Angular momentum

If we define angular momentum as the cross-product $\vec L=\vec r \times \vec p$, its magnitude is $L=r_\perp p$ (see the Cross-product skill). For a…

## Proof 32: Momentum conservation law

The moment conservation law and Newton’s 3rd law as well as the idea of impulse seem equivalent (they all describe impacts/collisions). And in fact the…

## Proof 31: Elastic-collision speed “conservation”

We call a collision elastic if the total kinetic energy is conserved (same before as after the collision) and there are no other energies involved.…

Our skills roadmaps have now been updated to a sleeker graphical style. A few examples: With the new style, we hope for better overview of…

The Rotation discipline has been launched this week! The skills roadmap is here: The discipline is split into two courses, of which the first one…

## Proof 8: The sum of squares

The formula for the sum of squares is: $$1^2+2^2+\cdots+n^2=\frac16 n(n+1)(2n+1)$$ It is useful because it converts a row of confusingly many terms (therefore the dots…

## Proof 7: Pyramid and cone volume

The Cheops pyramid in Egypt is constructed of many equally thick layers of box-shaped stones (more or less). Imagine more and more such layers being…

## Proof 6: Prism and cylinder volume

In a room with 3 metres to the ceiling, there are 3 cubic metres above each square metre floor regardless of the shape. The 3…