솔루션피아

$$\title{Rotational Inertia of Solid Disk}$$ $$ \sigma=\frac{\dd m}{\dd a}=\frac{M}{A}=\frac{M}{\pi R^2} \taag1$$ $$ \begin{aligned} l&=r\theta,\\ \dd l&=r \dd \theta\\ \end{aligned} $$ $$ \begin{aligned} \dd a&=\dd r \cdot \dd l\\ &=\dd r \cdot (r \dd\theta)\\ &=r\cdot\dd r \dd\theta\taag2\\ \end{aligned} $$ $$ \begin{aligned} \dd m&=\sigma\cdot\dd a\\ &=\sigma\cdot (r\dd r \dd\theta)\\ &=\sigm..

$$\title{Rotational Inertia of Hollow Cylinder}$$ $$r=R,$$ $$ \sigma=\frac{\dd m}{\dd a}=\frac{M}{A}=\frac{M}{LH}=\frac{M}{2\pi R H} \taag1$$ $$ \begin{aligned} l&=r\theta,\\ \dd l&=r\dd\theta\\ &=R\dd\theta\taag2 \end{aligned} $$ $$ \begin{aligned} \dd a&=\dd l\cdot\dd h \\ &=(R\dd\theta)\cdot\dd h \\ &=R\cdot\dd\theta\dd h \\ \end{aligned} $$ $$ \begin{aligned} \dd m&=\sigma\cdot\dd a\\ &=\sig..

$$\title{Rotational Inertia of Hoop}$$$$r=R,$$$$ \lambda=\frac{\dd m}{\dd l}=\frac{M}{L}=\frac{M}{2\pi r}=\frac{M}{2\pi R} \taag1$$$$ \begin{aligned}l&=r\theta,\\\dd l&=r\dd\theta\\&=R\dd\theta\taag2\end{aligned} $$$$$$$$ \begin{aligned} \dd m&=\lambda\cdot\dd l\\ &=\lambda\cdot (R\dd\theta)\\ &=\lambda R\cdot\dd\theta\taag3\\ \end{aligned} $$$$ \begin{aligned} \dd I&=r^2\cdot \dd m\\ &=R^2\cdot..

$$\title{About Taylor Series}$$ $$ \put \begin{cases} f(x)&=\text{Any Function}\\ g(x)&=c_0+c_1x+c_2x^2+\cdots+c_nx^n+\cdots \end{cases} $$ $$ \put \begin{cases} f(0)&=g(0)\\ f'(0)&=g'(0)\\ f''(0)&=g''(0)\\ &\vdots\\ f^{(n)}(0)&=g^{(n)}(0)\\ &\vdots\\ \end{cases} $$ $$ \begin{cases} g(x)&=c_0+c_1x+c_2x^2+\cdots\\ g'(x)&=c_1+2c_2x+3c_3x^2+\cdots\\ g''(x)&=2c_2+3\cdot2c_3x+4\cdot3c_3x^2+\cdots\\ &..