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The masses and coordinates of four particles are as follows: 77 g, x = 4.0 cm,...

The masses and coordinates of four particles are as follows: 77 g, x = 4.0 cm, y = 4.0 cm; 28 g, x = 0, y = 8.0 cm; 13 g, x = - 6.0 cm, y = - 6.0 cm; 64 g, x = - 4.0 cm, y = 8.0 cm. What are the rotational inertias of this collection about the (a) x, (b) y, and (c) z axes?

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Answer #1

We know that......

a)

Rotational inertia about X-axis are the ...

Ix = Total (Mi*yi^2)

Ix = m1*y1^2 + m2*y2^2 + m3*y3^2 + m4*y4^2

Put the values.....

Ix = 77*4^2 + 28*8^2 + 13*(-6)^2 + 64*(8)^2

Ix = 7588 gm-cm^2

b).

Similar condition of the ...

Rotational inertia about Y-axis are the....

Iy = Total (Mi*xi^2)

Iy = m1*x1^2 + m2*x2^2 + m3*x3^2 + m4*x4^2

Put the values.....

Iy = 77*4^2 + 28*0^2 + 13*(-6)^2 + 64*(-4)^2

Iy = 2724 gm-cm^2

c)

In this condition of the ...

Iz = Ix + Iy

Put the values.....

Iz = 7588 + 2724 = 10312 gm-cm^2 .   

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