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Find moment of inertia of a disc?

  • physics -

    if of a solid disc around an axis through the center and perpendicular to the surface (an axle)

    radius R, thickness t
    mass M = rho (volume) = rho(pi R^2 t)

    I = rho *t* integral 2 pi r^3 dr
    = t rho (2 pi)R^4/4 = t rho pi R^4/2

    but rho t = M/pi R^2
    so
    I = M R^2/2

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