Respuesta :
Answer:
(A). The rotational momentum of the flywheel is 12.96 kg m²/s.
(B). The rotational speed of sphere is 400 rad/s.
Explanation:
Given that,
Mass of disk = 10 kg
Radius = 9.0 cm
Rotational speed = 320 m/s
(A). We need to calculate the rotational momentum of the flywheel.
Using formula of momentum
[tex]L=I\omega[/tex]
[tex]L=\dfrac{1}{2}mr^2\omega[/tex]
Put the value into the formula
[tex]L=\dfrac{1}{2}\times10\times(9.0\times10^{-2})^2\times320[/tex]
[tex]L=12.96\ kg m^2/s[/tex]
(B). Rotation momentum of sphere is same rotational momentum of the flywheel
We need to calculate the magnitude of the rotational speed of sphere
Using formula of rotational momentum
[tex]L_{sphere}=L_{flywheel}[/tex]
[tex]I\omega_{sphere}=I\omega_{flywheel}[/tex]
[tex]\omega_{sphere}=\dfrac{I\omega_{flywheel}}{I_{sphere}}[/tex]
[tex]\omega_{sphere}=\dfrac{I\omega_{flywheel}}{\dfrac{2}{5}mr^2}[/tex]
Put the value into the formula
[tex]\omega_{sphere}=\dfrac{12.96}{\dfrac{2}{5}\times10\times(9.0\times10^{-2})^2}[/tex]
[tex]\omega_{sphere}=400\ rad/s[/tex]
Hence, (A). The rotational momentum of the flywheel is 12.96 kg m²/s.
(B). The rotational speed of sphere is 400 rad/s.
