## Phase Velocity of a Wave

A simple derivation of the phase velocity of a wave from the definition of the wavelength and the period.

Here you will learn the laws of **motion of bodies** (e.g. particles, cars, planets) under the influence of **mechanical forces**. Master the power to predict the future location and state of these bodies - whether the body is particle-like or wave-like.

A simple derivation of the phase velocity of a wave from the definition of the wavelength and the period.

` $$ y(x) ~=~ y_0 ~+~ \tan(\varphi_0) \, x ~-~ \frac{g}{2{v_0}^2 \, \cos(\varphi_0)^2 } \, x^2 $$ `

` $$ y ~=~ -\frac{g}{ 2\,{v_0}^2 } \, x^2 ~+~ y_0 $$ `

` $$ \class{green}{a_{\text c}} ~=~ 2 \, \class{red}{v} \, \class{brown}{\omega} \, \sin(\varphi) $$ `

` $$ v'_2 ~=~ v_1 \, \left( \frac{2m_1}{ m_1 + m_2 } \right) ~+~ v_2 \, \left( \frac{m_2 - m_1}{ m_1 + m_2 } \right) $$ `

Here you will learn the basics of special relativity, such as time dilation and length contraction, and how they are illustrated in spacetime diagrams.

Here you will learn the theoretical physics of classical mechanics, which has the goal of finding out the trajectory of a body.

` $$ I ~=~ \frac{2}{5} \, m \, r^2 $$ `

` $$ I ~=~ \frac{1}{2} \, m \, r^2 $$ `

` $$ I ~=~ m \, r^2 $$ `

Derivation of the moment of inertia of a homogeneous hollow cylinder and a solid cylinder rotating around its axis of symmetry.

` $$ \class{blue}{a_{\text{tan}}} ~=~ r \, \class{red}{\alpha} $$ `