91影视

$\begin{array}{c}\mathrm{m}=1.0\text{kg}\\ {\text{I}}_1=0.12\text{kg}.{\text{m}}^2\\ \mathrm{r}=0.60\text{m}\end{array}$

First, find the total rotational inertia. Using the law of conservation of angular momentum, find the final angular velocity.According tothe conservation of momentum, momentum of a system is constant if no external forces are acting on the system.

Formula are as follow:

${\mathrm{I}}_{\mathbf{2}}\mathbf{=}{\mathbf{I}}_{\mathbf{1}}\mathbf{+}{\mathbf{mr}}^{\mathbf{2}}$

$\mathbf{Initial}\mathbf{}\mathbf{angular}\mathbf{}\mathbf{momentum}\mathbf{=}\mathbf{Final}\mathbf{}\mathbf{angular}\mathbf{}\mathbf{momentum}$

Where,$\mathit{I}$is moment of inertia,$\mathit{m}$ is mass and $\mathit{r}$is radius.

According to law of conservation of angular momentum:

$\mathrm{Initial}\mathrm{angular}\mathrm{momentum}=\mathrm{Final}\mathrm{angular}\mathrm{momentum}$

$\begin{array}{c}{\mathrm{L}}_1={\mathrm{L}}_2\\ {\mathrm{I}}_1{\mathrm{蝇}}_1={\mathrm{I}}_2{\mathrm{蝇}}_2\end{array}$

$\begin{array}{c}{\mathrm{I}}_2={\mathrm{I}}_1+\mathrm{m}脳{\mathrm{r}}^2\\ {\mathrm{I}}_2=0.12+0.2脳{0.6}^2=0.3192\text{kg}.{\text{m}}^2\\ 0.12脳2.4=0.192脳{\mathrm{蝇}}_2\end{array}$

By solving above equation for ${\mathrm{蝇}}_2$,

${\mathrm{蝇}}_2=1.5\text{rad}/\text{s}$

Hence,angular speed after collision is$\mathrm{蝇}=1.5\frac{\text{rad}}{\text{s}}.$

Therefore, angular speed after collision can be calculated by using conservation of momentum principle.