Question

Compute the moment of inertia of the 100 mm × 150 mm rectangle shown in Fig. about x-x axis to which it is inclined at an angle

θ = sin^–1 \(\left(\frac45\right)\)

Answer 1

The rectangle is divided into four triangles as shown in the figure. [The lines AE and FC are parallel to x-axis].

Now θ = sin^–1 \(\left(\frac45\right)\) = 53.13°

From the geometry of the Fig. 

BK = AB sin (90° – θ) 

= 100 sin (90° – 53.13°) 

= 60 mm 

ND = BK = 60 mm

FD = \(\frac{60}{sin\,\theta}\) = \(\frac{60}{sin\,53.13}\) = 75 mm

∴ AF = 150 – FD = 75 mm 

Hence FL = ME = 75 sin θ = 60 mm

AE = FC = \(\frac{AB}{cos(90^\circ-\theta)}\) = \(\frac{100}{08}\) = 125 mm