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12 September, 08:34

A cylinder with rotational inertia I₁ = 2.4 kg · m² rotates clockwise about a vertical axis through its center with angular speed ω₁ = 5.8 rad/s. A second cylinder with rotational inertia I₂ = 1.3 kg · m² rotates counterclockwise about the same axis with angular speed ω₂ = 7.0 rad/s. If the cylinders couple so they have the same rotational axis, what is the angular speed of the combination (in rad/s) ?

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  1. 12 September, 11:04
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    Answers:

    Explanation:

    Given that.

    First cylinder data

    Inertial I₁ = 2.4 kgm²

    angular speed ω₁ = 5.8 rad/s.

    Second cylinder data

    inertia I₂ = 1.3 kgm²

    angular speed ω₂ = 7.0 rad/s.

    If the cylinders couple so they have the same rotational axis, what is the angular speed of the combination (in rad/s) ?

    So, the cylinder couple and move together with the same angular speed

    Then, using conservation of angular momentum

    L (final) = L (initial)

    (I₁ + I₂) • ω = I₁•ω₁ + I₂ω₂

    (2.4+1.3) •ω = 2.4 * 5.8 + 1.3 * 7

    3.7•ω = 23.02

    ω = 23.02 / 3.7

    ω = 6.22 rad/s

    The combine angular speed of the cylinder is 6.22 rad/s
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