Respuesta :
Answer:
[tex]\omega_f=12.2954 \,rad.s^{-1}[/tex] i.e.
[tex]Frequency=1.9569\,rev.s^{-1}[/tex]
Explanation:
Given:
angular speed,[tex]\omega_i =2\times 2\pi \,rad.s^{-1}[/tex]
mass of the disk, [tex]M=4.9\,kg[/tex]
radius of the disk, [tex]R=0.2\,m[/tex]
mass of the chunk, [tex]m=2.7\,kg[/tex]
radius of the chunk, [tex]r=0.04\,m[/tex]
We know that the angular momentum is given by:
[tex]L=I.\omega[/tex]
and moment of inertia for a disc:
[tex]I=\frac{1}{2} m.r^2[/tex]
According to the conservation of angular momentum, the final angular momentum is equal to the initial angular momentum.
[tex]\frac{1}{2} \times M.R^2\times \omega= \frac{1}{2} \times (M.R^2+m.r^2) \omega_f[/tex]
[tex]4.9\times 0.2^2\times (2\times 2\pi)=(4.9\times 0.2^2+2.7\times 0.04^2 )\tiems \omega_f[/tex]
[tex]\omega_f=12.2954 \,rad.s^{-1}[/tex]
[tex]Frequency=1.9569\,rev.s^{-1}[/tex]
