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Mass with Triple Integrals

Mass with Triple Integrals

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These are common formulas for finding mass of an object with triple integrals in terms of density.

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Items (15)

  • M (Mass)

    ∫∫∫density dV

  • Myz (First Moment about yz-plane)

    ∫∫∫x*density dV

  • Mxz (First Moment about xz-plane)

    ∫∫∫y*density dV

  • Mxy (First Moment about xy-plane)

    ∫∫∫z*density dV

  • x̄ (Center of Mass)

    Myz / M

  • ỹ (Center of Mass)

    Mxz / M

  • ź (Center of Mass)

    Mxy / M

  • Ix (Moment of Inertia about x-axis)

    ∫∫∫(y^2 + z^2)*density dV

  • Iy (Moment of Inertia about y-axis)

    ∫∫∫(x^2 + z^2)*density dV

  • Iz (Moment of Inertia about z-axis)

    ∫∫∫(x^2 + y^2)*density dV

  • IL (Moment of Inertia about a line L)

    ∫∫∫(r^2)*density dV

  • 2D: I0 (Moment of Inertia about the origin)

    Ix + Iy

  • 2D: I0 (Moment of Inertia about the origin)

    ∫∫(x^2 + y^2)*density dA

  • 2D: IL (Moment of Inertia about a line L)

    ∫∫(r^2)*density dA

  • r(x, y, z)

    distance from point (x, y, z) to line L