Question

Q. 1 Determine the moment of Inertia about given x and y axis in the following figure if a = 10 mm.​

Answer 1

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Answer 2

Given:

a = 10 mm

To find:

The moment of Inertia I =?

Explanation:

Moment of inertia is that a quantitative measure of the rotational inertia of a body.

1)The moment of Inertia of rectangle  = I1

lenghth of rectangle = l = 2a + a = 3a

breadth of rectangle = b = a + a = 2a

$\displaystyle I_1 = \frac{l \times b^3}{12}$

   = $\displaystyle \frac{(3a)(2a)^3}{12}$

$\mathbf{I_1}$ =  $\displaystyle \mathbf{2a^4}$ $\mathbf{m^4}$

2) The moment of Inertia of a semicircle:

radius of circle = r = a

$\displaystyle I_2 = \frac{\pi r^4}{8}$

   = $\displaystyle I_2 = \frac{\pi a^4}{8}$$\mathbf{m^4}$

$\mathbf{I_2}$ = 0.3925 $\displaysyle \mathbf{a^4}$

∴ The moment of inertia of shaded figure =  moment of inertia of rectangle - 2( moment of inertia of circle )

  I = $I_1 - 2I_2$

    = $2a^4 - 2(0.3925)a^4$

    = 1.1215 $(10)^4$                    ∵ a =10 mm

I = 12150 m$\mathbf{m^4}$

∴ The moment of inertia of the shaded figure is 12150 m$m^4$.