Answer:0.316 rad/s
Explanation:
Given
mass of Person [tex]m=65 kg[/tex]
velocity of person [tex]v=3.8 m/s[/tex]
diameter of turntable [tex]d=6.5 m[/tex]
moment of Inertia of the table [tex]I_0=1850 kg-m^2[/tex]
Moment of inertia of Person I
[tex]I=mr^2=65\times (\frac{6.5}{2})^2[/tex]
[tex]I=686.56 kg-m^2[/tex]
initial angular velocity [tex]\omega _1=\frac{v}{r}[/tex]
[tex]\omega _1=\frac{3.8}{3.25}=1.17 rad/s[/tex]
Conserving Angular momentum
[tex]I\omega _1=(I+I_0)\omega _2[/tex] , where [tex]\omega _2=final\ angular\ velocity[/tex]
[tex]686.56\times 1.17=(686.56+1850)\times \omega _2[/tex]
[tex]\omega _2=\frac{686.56}{2536.56}\times 1.17[/tex]
[tex]\omega _2=0.316 rad/s[/tex]
