Answer:
New angular speed changes from 16 rpm to 19.95 rpm
Explanation:
In the given system the angular momentum of the system is conserved
initial angular momentum of the system
[tex]L_{i}=I_{1}\omega _{1}\\\\\omega _{1}=\frac{8\pi }{15}rad/sec\\\\I_{1}=\frac{1}{2}mr^{2}+(m_{1}+m_{2}+m_{3})r^{2}\\\\I_{1}=\frac{1}{2}\times 105\times 1.8^{2}+(33+28+28) \times 1.8^{2}=458.46kgm^{2}\\\\\therefore L_{i}=458.46\times \frac{8\pi }{15}=768.16[/tex]
When 28 kg child moves to the center the moment of inertia changes thus we have
[tex]I_{2}=\frac{1}{2}mr^{2}+(m_{1}+m_{2})r^{2}\\\\I_{1}=\frac{1}{2}\times 105\times 1.8^{2}+(33+28) \times 1.8^{2}=367.74kgm^{2}\\\\\therefore L_{f}=367.74\times \omega _{f}[/tex]
Equating initial and final angular momentum we get
[tex]I_{2}=\frac{1}{2}mr^{2}+(m_{1}+m_{2})r^{2}\\\\I_{1}=\frac{1}{2}\times 105\times 1.8^{2}+(33+28) \times 1.8^{2}=367.74kgm^{2}\\\\\therefore L_{f}=367.74\times \omega _{f}\\\\\omega _{f}=\frac{768.16}{367.74}=2.1rad/sec\\\\N_{2}=19.95rpm[/tex]
