Given
Mass of the three particles,
[tex]\begin{gathered} m_1=7.3\text{ kg} \\ m_2=9.5\text{ kg} \\ m_3=9.7\text{ kg} \end{gathered}[/tex]
Their respective coordinates are:
[tex]\begin{gathered} (x_1,y_1)=(3,-4) \\ (x_2,y_2)=(-11,4) \\ (x_3,y_3)=(8,1) \end{gathered}[/tex]
The angular velocity is
[tex]\omega=21\text{ rad/s}[/tex]
To find
The angular momentum
Explanation
Moment of inertia about the y-axis
[tex]\begin{gathered} I=m_1x_1^2+m_2x_2^2+m_3x_3^2 \\ \Rightarrow I=7.3\times3^2+9.5\times(-11)^2+9.7\times8^2 \\ \Rightarrow I=1836\text{ kgm}^2 \end{gathered}[/tex]
The angular momentum is
[tex]\begin{gathered} L=I\omega \\ \Rightarrow L=1836\times21=38556\text{ Js} \end{gathered}[/tex]
Conclusion
The angular momentum is B.38556 Js
