Respuesta :
Answer
given,
diameter of merry - go - round = 3 m
mass of the disk = 290 kg
speed of the merry- go-round = 25 rpm
speed = 5.6 m/s
mass of John = 30 kg
[tex]I_{disk} = \dfrac{1}{2}MR^2[/tex]
[tex]I_{disk} = \dfrac{1}{2}\times 290 \times 1.5^2[/tex]
[tex]I_{disk} = 326.25 kg.m^2[/tex]
initial angular momentum of the system
[tex]L_i = I\omega_i + mvR[/tex]
[tex]L_i =326.25 \times 25 \times \dfrac{2\pi}{60} + 30 \times 5.6 \times 1.5[/tex]
[tex]L_i =1106.12\ kg.m^2/s[/tex]
final angular momentum of the system
[tex]L_f = (I_{disk}+mR^2)\omega_{f}[/tex]
[tex]L_f = (326.25 + 30\times 1.5^2)\omega_{f}[/tex]
[tex]L_f= (393.75)\omega_{f}[/tex]
from conservation of angular momentum
[tex]L_i = L_f[/tex]
[tex]1106.12 = (393.75)\omega_{f}[/tex]
[tex]\omega_{f}=2.809 \times \dfrac{60}{2\pi}[/tex]
[tex]\omega_{f}=26.82\ rpm[/tex]
