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Calculate the moment of inertia of a hol...

Calculate the moment of inertia of a hollow cylinder of mass M and radius R about a line parallel to the axis of the cylinder and on the surface of the cylinder?

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To calculate the moment of inertia of a hollow cylinder of mass \( M \) and radius \( R \) about a line parallel to the axis of the cylinder and on the surface of the cylinder, we can follow these steps: ### Step 1: Understand the Geometry A hollow cylinder can be visualized as a cylindrical shell with a certain mass and radius. The moment of inertia (I) is a measure of how difficult it is to change the rotational motion of the object about a given axis. ### Step 2: Moment of Inertia about the Central Axis The moment of inertia of a hollow cylinder about its central axis (which is perpendicular to the circular faces) is given by the formula: \[ ...
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Knowledge Check

  • Moment of inertia of a hollow cylinder of mass M and radius r about its own axis is

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

  • Moment of inertia of a hollow cylinder of mass M and radius R , about the axis of cylinder is

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

  • The moment of inertia of cylinder of radius a, mass M and height h about an axis parallel to the axis of the cylinder and distance b from its centre is :

    A
    `(1)/(2)M(a^(2)+2b^(2))`
    B
    `(1)/(2)M(2a^(2)+b^(2))`
    C
    `(1)/(2)M(a^(2)+b^(2))`
    D
    `(1)/(2)M(a^(2)/(3)+(b^(2))/(12))`

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