Table 102

Mass Properties of Geometric Shapes

This table provides formula for calculating mass and mass moment of inertia for various geometric shapes. The constant for the acceleration of gravity, g, is in length/time^2 when the density, rho, is given as a weight density in units of force/length^3. If the density is given in units of mass per unit volume, the correction for the acceleration of gravity is not required.

Formula for Bar, Disk, Rectangular Prism, Full Cylinder and Hollow Cylinder is provided.

Mass Properties of Shapes
Nomenclature:

rho = density, weight/unit volume 

m = mass

I = mass moment of inertia, 

g = acceleration of gravity, = length/time^2 when density is given as 
force/unit volume (ie. weight/unit volume). 

Rod relationships:
------------------
m = (3.14159 / 4)  *( d^2 * l) * (rho / g) => See Nomenclature Above
Iy = m * l^2 / 12
Iz = m * l^2 / 12
Ix = m * d^2 / 8

Round disk relationships:
-------------------------
m = (3.14159 / 4) * (d^2 * t) * (rho / g) => See Nomenclature Above
Iy = m * d^2 / 16
Iz = m * d^2 / 16
Ix = m * d^2 / 8

Rectangular prism relationships:
--------------------------------
m = (a * b * c) * (rho / g) => See Nomenclature Above
Iy = m / 12 * (a^2 + c^2)
Iz = m / 12 * (b^2 + c^2)
Ix = m / 12 * (a^2 + b^2)

Cylinder relationships:
-----------------------
m = (3.14159 /4) * (d^2 * l) * (rho / g) => See Nomenclature Above
Iy = m / 48 * (3 * d^2 + 4 * l^2)
Iz = m / 48 * (3 * d^2 + 4 * l^2)
Ix = m * d^2 / 8

Hollow Cylinder relationships:
------------------------------
m = (3.14159 / 4) * ((d0^2 - di^2)*L) * (rho/g) => See Nomenclature Above
Iy = m / 48 * (3 * d0^2 + 3 * di^2 + 4 * l^2)
Iz = m / 48 * (3 * d0^2 + 3 * di^2 + 4 * l^2)
Ix = m / 8 * (d0^2 + di^2)

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Last update - 3/19/2005