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State the expression for the moment of i...

State the expression for the moment of inertia of a thin uniform disc about an axis perpendicular to its plane and through its centre. Hence deduce the expression for its moment of inertia about a tangential axis perpendicular to its plane.

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To find the moment of inertia of a thin uniform disc about an axis perpendicular to its plane and through its center, we start with the known formula for the moment of inertia of a disc. ### Step 1: Moment of Inertia of a Thin Uniform Disc The moment of inertia \( I \) of a thin uniform disc about an axis perpendicular to its plane and through its center is given by the formula: \[ I = \frac{1}{2} M R^2 \] where: ...
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Knowledge Check

  • The moment of inertia of a thin uniform rod of mass M and length L about an axis perpendicular to the rod, through its centre is I . The moment of inertia of the rod about an axis perpendicular to rod through its end point is

    A
    `I/4`
    B
    `I/2`
    C
    `2I`
    D
    `4I`

  • Moment of inertia of a thin uniform rod about an axis passing through one end perpendicular to its length is I . Then moment of inertia the same rod about the central axis perpendicular to its plane is

    A
    `I//4`
    B
    2I
    C
    4I
    D
    3 I

  • The moment of inertia of a thin uniform rod of mass M and length l about an axis perpendicular to the rod through its centre is I. The moment of inertia of the rod through its end point is

    A
    `(I)/(4)`
    B
    `(I)/(2)`
    C
    `2I`
    D
    `4I`

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