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17 August, 10:28

Calculate the rotational inertia of each of the following uniform objects about the axes indicated: a) A thin 2.5 kg rod of length 0.75 m, about an axis perpendicular to it and passing through its center. b) A 3 kg thin walled hollow sphere 0.38 m in diameter, about an axis (i) through its center, and (ii) tangent to the edge of the sphere

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  1. 17 August, 13:03
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    a. I₁ = 0.1171875 kg * m²

    b. I₂ = 0.288 kg * m²

    Explanation:

    a. m₁ = 2.5 kg, L₁ = 0.75 m

    The rotational inertia about an axis perpendicular to it and passing through its center

    I₁ = ¹/₁₂ * M * L²

    I₁ = ¹/₁₂ * 2.5 kg * (0.75m) ²

    I₁ = 0.1171875 kg * m²

    b. m₂ = 3 kg, d₁ = 0.38 m

    The rotational inertia tangent to the edge of the sphere

    I₂ = ²/₃ * M * R²

    I₂ = ²/₃ * 3 kg * (0.38m) ²

    I₂ = 0.288 kg * m²
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