Balder W. Holst

Hello there!

My name is Balder and this is my personal website. Here i write down what i learn to maybe help others some day. For now i will just act like people are reading my articles, and make them for fun.

This website has three main sections:

I write these articles for fun, and even though i try to make sure that they are correct, i am not a perfect human and there are sure to be mistakes. Below is a list of most recent articles in all categories.

Recent Posts

Relativitetsteorien
Relativitetsteorien $$E=m \cdot c^2$$ Kinetisk energi for en partikel $$K_{kin}=m \cdot c^2-m_0 \cdot c^2$$ $m$: >Relativitsisk masse $m_0$: Massen når partiklen er i hvile
0001/01/01 · Notes
Riemann Sum
Riemann Sum In two dimensions the area can be approximated by dividing the $xy$-plane into squares, and finding the function value in the middle of each column. At last summing up their volumes yields an approximation of the area under the surfaceo.
0001/01/01 · Notes
RMS-værdien
RMS-værdien “Ækvivalent for tidsvarierende signal (> AC> > $\rightarrow$> > DC> )" - Jan Bruges til at beregne effektafsættelse Formler $$V_{RMS}= V_{DC} =\sqrt{ \frac{1}{T} \cdot \int_{0}^{T} v^{2}(t) \text{dt} }$$ $$V_{RMS}= \frac{v_{max}}{\sqrt{2}}$$
0001/01/01 · Notes
Rotation
Rotation Se slideshow. Relevante noter Inertimoment Kraftmoment $$\theta(t)$$ $\theta(t)$ : Vinkel som funktion af tid. Øjeblikkelig vinkelhastighed Vi kan selvfølgelig differentiere $\theta(t)$ for at få vinkel-hastigheden. $$\vec{\omega} = \frac{d \theta(t)}{dt} \hat{\omega}$$ $\hat{\omega}$ : Enhedsvektor (Peger “op” ad tommelfingeren med højrehåndsmetoden) $\vec{\omega}$ : Vinkelhastigheden til tiden $t$. Konstant vinkelhastighed $$\theta(t) = \theta_{0} + \omega_{0} \cdot t$$ Vinkelacceleration Igen kan vinkelhastigheden differentieres for at få vinkelaccelerationen. $$\vec{\alpha} = \frac{d \omega(t)}{dt} \cdot \hat{\omega} = \frac{d^{2} \theta}{dt^{2}} \cdot \hat{\omega}$$
0001/01/01 · Notes
Rotational Matrices
Rotational Matrices A way to translate rotation between frames. Assuming that we are working in three dimensions, the rotational matrix will always be in $\R^{3 \times 3}$ space. $$^{A}{B} R = \left[^{A}\hat{X}{B} ,,^{A}\hat{Y}{B} ,, ^{A}\hat{Z}{B} \right] = \left( \begin{array}{ccc} r_{11} & r_{12} & r_{13} \ r_{21} & r_{22} & r_{23} \ r_{31} & r_{32} & r_{33} \ \end{array} \right)$$ The columns are the unit vectors of $\set{B}$ seen from $\set{A}$.
0001/01/01 · Notes
Row Echelon Form
Row Echelon Form Pivot-elementet i en række er altid til højre for pivot elementet i rækken over. Pivot-element: første ikke-nul i en række. Ønske: altid nuller under og under-til-venstre. Eksempler $$ >\left( >\begin{array}{cccc|c} > 2 & 1 & -2 & 3 & 1 \ > 0 & 1 & 2 & 2 & 2 \ > 0 & 0 & 0 & 1 & 3 \ >\end{array} >\right) >$$ $$\left( >\begin{array}{ccc} > 2 & 3 & 1 \ > 0 & -1 & 2 \ > 0 & 0 & 1 \ >\end{array} >\right)$$ Dette er også ok $$\left( >\begin{array}{cccc} > 1 & 2 & 3 & 4 \ > 0 & 5 & 6 & 7 \ > 0 & 0 & 0 & 0 \ >\end{array} >\right)$$
0001/01/01 · Notes
Rulning
Rulning “Rulning er en kombination af > Rotation> og translation” - Rene (> slide> ) $$\omega = \frac{v}{R}$$ $$v_{top} = 2R \omega = 2v$$ Vinkelaccerationen (slide) $$\alpha = \frac{MgR\sin(\theta)}{MR^{2}+I}$$ Hastighed $$v = R \omega = v_{0} + g \sin(\theta) \frac{MR^{2}}{MR^{2}+I} \cdot t$$ Brøken er $1$ hvis objektet ikke ruller. Brøken kan også omskrives således $$\frac{1}{1+c} \s \text{hvor } I=cMR^2$$ $c$ kan findes for foeskellige objekter i tabellen for inertimomenter.
0001/01/01 · Notes
Række og Søjle vektorer
Række og Søjle vektorer Kolonnevektor $$v_{n\times 1} = \left( {\begin{array}{cccc} v_{1}\ v_{2}\ \vdots\ v_{n}\ \end{array} } \right) $$ Rækkevektor $$v_{1\times n} = \left( {\begin{array}{cccc} v_{1} & v_{2} & \dots & v_{n} \end{array} } \right) $$
0001/01/01 · Notes
Røntgenrør
Røntgenrør $$\lambda_{min} = \frac{h \cdot c}{e \cdot U_0}$$ $\lambda_{min}$: Den $h$: Planck konstanten $c$: Lysets Hastighed $e$: Elementarladningen $U_0$:
0001/01/01 · Notes
Røntgenstråling
Røntgenstråling Kan dannes i Røntgenrør Røntgenspektrum Formler $$h \cdot f_{maks}=e \cdot U \arrows f_{maks}=\frac{e \cdot U}{h}$$ $$2 \cdot \lambda_{min} \cdot f_{maks}=c \arrows \lambda_{min} = \frac{c}{f_{maks}}$$ $$\lambda_{min} = \frac{c}{\frac{e \cdot U}{h}=c \cdot \frac{h}{e \cdot u}}=\frac{h \cdot c}{e \cdot U}$$ $$\Updownarrow$$ $$\lambda_{min}=\frac{h \cdot c}{e \cdot U}$$
0001/01/01 · Notes