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Radius of gyration




Radius of gyration

  • Whatever may be the shape of the body it is always possible to find a distance from the axis of rotation at which whole mass of the body can be assumed to be concentrated and even then its moment of inertia about that axis remains unchanged.
  • If whole mass of the body is supposed to be concentrated at a distance k from the axis of rotation then
    I=Mk2=Σmr2
    or ,
    k=√(I/M)=√(Σmr2/M)
    This quantity k is called radius of gyration of the body about the axis of rotation.
  • Thus, the radius of gyration of a body, rotating about a given axis of rotation is the radial distance from the axis and when the square of radius of gyration (k) is multiplied by the total mass of the body it gives the moment of inertia of the body about that axis.

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