Respuesta :
Answer:
[tex]N=285711.106\,rpm[/tex]
Explanation:
Given:
energy to be stored in a flywheel, [tex]E=1.1\times 10^9\,J[/tex]
mass of the flywheel, [tex]m=12\,kg[/tex]
radius of the flywheel, [tex]r=0.32\,m[/tex]
To find:
rotational speed, N=?
We know that kinetic energy of a flywheel can be given by:
[tex]KE=\frac{1}{2} I.\omega^2[/tex].................................(1)
&
[tex]I=m.r^2[/tex]......................................(2)
where:
I=moment of inertia
[tex]\omega [/tex]= angular velocity in radian per second
putting respective values in eq. (2)
[tex]I=12\times 0.32^2[/tex]
[tex]I=1.2288 \,kg.m^2[/tex]
Now, from eq. (1)
[tex]E=\frac{1}{2} \times I.\omega^2[/tex]
[tex]1.1\times 10^9=1.2288\times \omega^2[/tex]
[tex]\omega=29919.5971 \,rad.s^{-1}[/tex]
∵ [tex]\omega=\frac{ 2\pi.N}{60}[/tex]
[tex]N=\frac{29919.5971\times 60}{2\pi}[/tex]
[tex]N=285711.106\,rpm[/tex]
