Moments of Inertia
Example: Calculate the moment of inertia of area for the trapezoidal area, BCDE, shown
below about the z-axis, Izz = ʃ y2 dA
Strategy: Determine the limits of integration. Then use a double integral to evaluate Izz .
z = 1 y = z + 1
Izz = ʃ ʃ y2 dy dz
z = 0 y = 0
z = 1 z + 1
Izz = ʃ (1/3) y3 | dz
z = 0 0
z = 1
Izz = ʃ (1/3) [ z3 + 3z2 + 3z + 1 ] dz
z = 0
1
Izz = (1/3) [ z4/4 + z3 + 3z/2 + z ] | = 5/4 (result)
0
Click here to return to discussion of moments of inertia.
Return to Notes on Statics
Copyright © 2019 Richard C. Coddington All rights reserved.