Respuesta :
Answer:[tex]\omega _f=1.185\ rad/s[/tex]
Explanation:
Given
mass of objects [tex]m=5\ kg[/tex]
Initially mass is at [tex]r=0.9\ m[/tex]
Initial angular speed [tex]\omega_i=0.66\ rad/s[/tex]
Moment of inertia of student and stool is [tex]I_s=8\ kg-m^2[/tex]
Finally masses are at a distance of [tex]r_f=0.31\ m[/tex] from axis
[tex]I_i=I_p+I_m[/tex]
[tex]I_i=8+2\times 5\times (0.9)^2[/tex]
[tex]I_i=16.1\ kg-m^2[/tex]
Final moment of inertia of the system
[tex]I_f=I_s+I_m[/tex]
[tex]I_f=8+2\times 5\times (0.31)^2[/tex]
[tex]I_f=8+0.961=8.961\ kg-m^2[/tex]
As there is no external torque therefore moment of inertia is conserved
[tex]I_i\omega _i=I_f\omega _f[/tex]
[tex]\omega _f=\frac{16.1}{8.96}\times 0.66[/tex]
[tex]\omega _f=1.796\times 0.66[/tex]
[tex]\omega _f=1.185\ rad/s[/tex]
