The masses and coordinates of four particles are indicated in the following tabl

Question

The masses and coordinates of four particles are indicated in the following table. (a) What is the rotational inertia of this collection about the x axis? gcm2(b) What is the rotational inertia of this collection about the y axis? gcm2(c) What is the rotational inertia of this collection about the z axis?
gcm2 (d) Suppose the answers to (a) and (b) are A and B, respectively. Then what is the answer to (c) in terms of A and B? A + B (A + B)2 A - B AB

25 g x = -3.0 cm y = -1.0 cm
40 g x = 2.0 cm y = -5.0 cm
25 g x = 0.0 cm y = 0.0 cm
25 g x = 1.0 cm y = -3.0 cm

Explanation / Answer

a)about x-axis= my2 = 25 x 12 + 40 x 52 + 25 x 02 + 25 x 32 = 1250g.cm2

b) about y-acis = mx2 = 25 x 32 + 40 x 22 + 25 x 0 x 25 x 12 = 410 g.cm2

c) about z-axis = m(x2 + y2 ) = mx2 + my2 = 410 + 1250 = 1660 g.cm2

d) = A + B

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