91影视

$\begin{array}{l}\mathrm{L}=0.6\text{m}\\ {\mathrm{n}}_1=0.5\text{rev}\\ {\mathrm{n}}_2=1.0\text{rev}\end{array}$

Calculate the angular speed of arms by using revolutions and time. Then, calculate angular momentum due to each arm to find the total angular momentum.

Formula are as follow:

1. $\mathbf{蝇}\mathbf{=}\frac{\mathbf{2}\mathbf{蟺}\mathbf{}\mathbf{脳}\mathbf{}\mathbf{Number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{revolutions}}{\mathbf{T}}$
   
2. $\mathbf{Initial}\mathbf{}\mathbf{angular}\mathbf{}\mathbf{momentum}\mathbf{=}\mathbf{Final}\mathbf{}\mathbf{angular}\mathbf{}\mathbf{momentum}$
   

Angular velocity is equal to the angular displacement per unit time. For each revolution, arm would cover $2\mathrm{蟺}$rad. So, if the number of revolutions of the arm are known in known time, the angular velocity can be found as,

$\mathrm{蝇}=\frac{2\mathrm{蟺}脳\mathrm{Number}\mathrm{of}\mathrm{revolutions}}{\mathrm{T}}$

Therefore, angular speed of arms,

$\begin{array}{l}{\mathrm{蝇}}_1=\frac{2{\mathrm{蟺苍}}_1}{0.7}=\frac{2\mathrm{蟺}脳0.5}{0.7}=4.49\frac{\text{rad}}{\text{s}}\\ {\mathrm{蝇}}_2=\frac{2{\mathrm{蟺苍}}_2}{0.7}=\frac{2\mathrm{蟺}脳1.0}{0.7}=8.98\frac{\text{rad}}{\text{s}}\end{array}$

Angular momentum of each arm,

$\begin{array}{l}{\mathrm{L}}_1={\mathrm{I}}_1{\mathrm{蝇}}_1=4脳{0.6}^2脳4.49=6.46{\text{kgm}}^{\text{2}}\text{/s}\\ {\mathrm{L}}_1={\mathrm{I}}_1{\mathrm{蝇}}_1=4脳{0.6}^2脳8.98=12.92{\text{kgm}}^{\text{2}}\text{/s}\end{array}$

Here, one arm rotates clockwise and other rotates anticlockwise. Hence, total angular momentum about the common rotation axis through the shoulders is,

$\mathrm{L}={\mathrm{L}}_2鈭�{\mathrm{L}}_1=12.92鈭�6.46=6.46\text{kg}\frac{{\text{m}}^{\text{2}}}{\text{s}}$

Hence,the magnitude of the total angular momentum of the arms of athlete is $\mathrm{L}=6.46\left({\text{kg.m}}^{\text{2}}\right)\text{/s}$.

Therefore, using the formula for the angular velocity and law of conservation of angular momentum, the total angular momentum of two arms can be found with reference to athlete鈥檚 body.