A 10-kg disk-shaped flywheel of radius 9.0 cm rotates with a rotational speed of 320 rad/s. Part A Determine the rotational momentum of the

Question

A 10-kg disk-shaped flywheel of radius 9.0 cm rotates with a rotational speed of 320 rad/s. Part A Determine the rotational momentum of the flywheel. Express your answer to two significant figures and include the appropriate units. Part B With what magnitude rotational speed must a 10-kg solid sphere of 9.0 cm radius rotate to have the same rotational momentum as the flywheel? Express your answer to two significant figures and include the appropriate units.

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Adela 1 year 2021-09-04T01:28:59+00:00 1 Answers 1 views 0

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    2021-09-04T01:30:31+00:00

    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.

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