 ## 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…

## 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.…