The moments of inertia of the area A about the parallel p an

The moments of inertia of the area A about the parallel p- and p\'-axes differ by 19(10⁶) mm⁴. Compute the area A which has its centroid at C.

Appendix A, Supplemental Problem A/005 The moments of inertia of the area A about the parallel p- and p-axes differ by 19(106 mm4. Compute the area A which has its centroid at C. 25 mm 42 mm Answer: A mm the tolerance is +/-2%

Solution

By parallel axis theorem:

I₁ =I₀ + mr₁²

similarly for r2

r1 = 42mm, r2 =67 mm

Let I₀ be the mI about centroid

Then taking the two MI by parallel axis Theorem, and subtracting

A*(67)² -A (42)² =19*10⁶

A= 6972.47 mm²