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Define Moment of Inertia....

Define Moment of Inertia.

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Moment of Inertia is defined as the product of mass of the rigid body and square of the radius of gyration. `I=MK^2kgm^2`
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Explore conceptually related problems

Define a moment of inertia. Obtain an expression for it

(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be 2MR^(2)//5 , where M is the mass of the sphere and R is the radius of the sphere. (b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be MR^(2)//4 , find its moment of inertia about an axis normal to the disc and passing through a point on its edge.

Knowledge Check

  • A circular disc X of radius R is made from an iron plate of thickness t, and another disc Y of radius 4R is made from an iron plate of thickness (t)/(4) . Then the relation between the moment of inertia I_(X) and I_(Y) is :

    A
    `I_(Y)=64I_(X)`
    B
    `I_(Y)=32I_(X)`
    C
    `I_(Y)=16I_(X)`
    D
    `I_(Y)=I_(X)`

  • If I_(1) is the moment of inertia of a thin rod about an axis perpendicular to its length and passing through its centre of mass, and I_(2) is the moment of inertia (about central axis) of the ring formed by bending the rod, then

    A
    `I_(1):I_(2)=1:1`
    B
    `I_(1):I_(2)=pi^(2):3`
    C
    `I_(1):I_(2)=pi:4`
    D
    `I_(1):I_(2)=3:5`

  • The moment of inertia of circular disc about its diameter is 200 g cm^(2) . Then its moment of inertia about an axis passing through its centre and normal to its face is :

    A
    `100gcm^(2)`
    B
    `200gcm^(2)`
    C
    `400gcm^(2)`
    D
    `1000gcm^(2)`

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    Define moment of force or torque.

    State whether moment of inertia is a scalar or a vector physical quantity

    What is the moment of inertia of a ring about a tangent to the circle of the ring?

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