Table 102

Mass Properties of Geometric Shapes

This table provides formula for calculating mass and mass moment of inertia for various geometric shapes.

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

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

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

Rectangular prism relationships:
--------------------------------
m = a * b * c * rho / g 
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 * d^2 * l * rho / (4 * g) 
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 * l * rho / (4 * g) * (d0^2 - di^2)
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)