Question

Need help on number 5. Super complex have had tutors that can’t solve

Answer 1

Given

Mass of the particles,

`\begin{gathered} m_1=10.3\text{ kg} \\ m_2=2.5\text{ kg} \\ m_3=2.7\text{ kg} \end{gathered}`

Their respective coordinates are

`\begin{gathered} (x_1,y_1)=(-12,-5) \\ (x_2,y_2)=(4,3) \\ (x_3,y_3)=(14,1) \end{gathered}`

The angular velocity is

`\omega=15\text{ rad/s}`

To find

Rotational kinetic energy of the system

Step-by-step explanation

The moment of inertia about the y axis is

`\begin{gathered} I=m_1x_1^2+m_2x_2^2+m_3x_3^2 \\ \Rightarrow I=10.3*12^2+2.5*4^2+2.7*^14^2 \\ \Rightarrow I=2052.4\text{ kgm}^2 \end{gathered}`

The rotational kinetic energy is

`\begin{gathered} K=(1)/(2)I\omega^2 \\ \Rightarrow K=(1)/(2)*2052.4*15^2 \\ \Rightarrow K=230895J \end{gathered}`

Conclusion

The rotational kinetic energy is A.230895 J