Consider four objects, each having the same mass and the same radius: 1. a solid sphere 2. a hollow sphere 3. a f

Question

Consider four objects, each having the same mass and the same radius:

1. a solid sphere
2. a hollow sphere
3. a flat disk in the x,y plane
4. a hoop in the x,y plane
The order of increasing rotational inertia about an axis through the center of mass and parallel to the z axis is:

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Acacia 3 days 2021-07-19T06:23:08+00:00 1 Answers 1 views 0

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    2021-07-19T06:24:43+00:00

    Answer:

    1. Solid Sphere: 0.4 kg m²

    2. Flat Disk in x,y plane: 0.5 kg m²

    3. A Hollow Sphere: 0.67 kg m²

    4. Hoop in x,y plane: 1 kg m²

    Explanation:

    The formulae for the rotation inertia of given shapes about z-axis are given as follows:

    1. Solid Sphere: (2/5)(MR²)

    2. A Hollow Sphere: (2/3)(MR²)

    3. Flat Disk in x,y plane = (1/2)(MR²)

    4. Hoop in the x,y plane = MR²

    where,

    M = mass

    R = Radius

    Since, it is stated that all shapes have same mass and radius. Therefore, we assume a mass of 1 kg and radius of 1 m for each shape. Hence values become:

    1. Solid Sphere: (2/5)(1 kg)(1 m)²

    2. A Hollow Sphere: (2/3)(1 kg)(1 m)²

    3. Flat Disk in x,y plane = (1/2)(1 kg)(1 m)²

    4. Hoop in the x,y plane = (1 kg)(1 m)²

    Solving the values, we get:

    1. Solid Sphere: 0.4 kg m²

    2. A Hollow Sphere: 0.67 kg m²

    3. Flat Disk in x,y plane = 0.5 kg m²

    4. Hoop in the x,y plane = 1 kg m²

    Therefore, it is clear from above calculations, that the order of increasing of rotational inertia of these shapes will be as follows:

    1. Solid Sphere: 0.4 kg m²

    2. Flat Disk in x,y plane: 0.5 kg m²

    3. A Hollow Sphere: 0.67 kg m²

    4. Hoop in x,y plane: 1 kg m²

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