$$

$3$ L $,$ R $.$

$$L$P.$

$$ no$-$slip$.$

$$

$..$

$(1)u(r{)}_{?}$

$.$

$[$:$u(r)=\frac{R^2}{4}[1-{}^{(b)}{]}^2+(c)\}$

$(2).$

$20\%$

$R.$

$z-.$

$(\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{t}}+u_r\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{r}}+\frac{u_{}}{r}\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}}+u\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{z}})=[\frac{1}{r}\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{r}}(r\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{r}})+\frac{1}{r^2}\frac{de{l}^{2}u}{\text{d}\text{e}\text{l}{}^2}+\frac{de{l}^{2}u}{del{z}^2}]-\frac{\text{d}\text{e}\text{l}\text{p}}{\text{d}\text{e}\text{l}\text{z}}+g_z$