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Calculate the moment of inertia of a dis...

Calculate the moment of inertia of a disc of radius R and mass M, about an axis passing through its centre and perpendicular to the plane.

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To calculate the moment of inertia (I) of a disc of radius R and mass M about an axis passing through its center and perpendicular to the plane, we can follow these steps: ### Step 1: Understand the Definition of Moment of Inertia The moment of inertia of a body is defined as the sum of the products of the mass elements and the square of their distances from the axis of rotation. Mathematically, it is given by: \[ I = \int r^2 \, dm \] where \( r \) is the distance from the axis of rotation to the mass element \( dm \). ...
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Knowledge Check

  • Moment of inertia of a ring of mass M and radius R about an axis passing through the centre and perpendicular to the plane is

    A
    `1//2MR^(2)`
    B
    `MR^(2)`
    C
    `1//4MR^(2)`
    D
    `3//4 MR^(2)`

  • The moment of inertia of a copper disc, rotating about an axis passing through its centre and perpendicular to its plane

    A
    increases if its temperature is increased
    B
    changes if its axis of rotation is changed
    C
    increases if its angular velocity is increased
    D
    both (a) and (b) are correct

  • Moment of inertia of a uniform quarter disc of radius R and mass M about an axis through its centre of mass and perpendicular to its plane is :

    A
    `(MR^(2))/(2)-M((4R)/(3pi))^(2)`
    B
    `(MR^(2))/(2)-M(sqrt(2)(4R)/(3pi))^(2)`
    C
    `(MR^(2))/(2)+M((4R)/(3pi))^(2)`
    D
    `(MR^(2))/(2)+M(sqrt(2)(4R)/(3pi))^(2)`