Respuesta :
Answer:
The angular velocity is [tex]2.64\times 10^{5}\ rev/min[/tex]
Solution:
As per the question:
Energy produced by gasoline, E = [tex]2.67\times 10^{9}[/tex]
Mass of the flywheel, m = [tex]38.3\ kg[/tex]
Radius of the flywheel, R = 0.363 m
Now,
The moment of Inertia of the disc is given by:
[tex]I = \frac{1}{2}mR^{2}[/tex]
[tex]I = \frac{1}{2}\times 38.3\times 0.363^{2} = 6.95\ kg-m^{2}[/tex]
Now, the angular velocity can be calculated as:
[tex]E = \frac{1}{2}I\omega ^{2}[/tex]
[tex]\omega = \sqrt{\frac{2E}{I}}[/tex]
[tex]\omega = \sqrt{\frac{2\times 2.67\times 10^{9}}{6.95}} = 27719\ rad/s[/tex]
Now,
1 revolution = [tex]2\pi\ rad[/tex]
Now,
[tex]\omega = \frac{27719\times 60}{2\pi} = 2.64\times 10^{5}\ rev/min[/tex]
