The masses and coordinates of four particles are indicated in the following tabl
ID: 2177870 • Letter: T
Question
The masses and coordinates of four particles are indicated in the following table.20 g x = 0.0 cm y = -3.0 cm
30 g x = 4.0 cm y = -3.0 cm
40 g x = 2.0 cm y = 0.0 cm
50 g x = 0.0 cm y = 2.0 cm
(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.AB
b.(A + B)2
c.A - B
d.A + B
Explanation / Answer
We know rotational inertia = mr2
(a) Distance from x-axis to a point will be y-coordinates
Ix = 20*(-3)2 +30*(-3)2 + 40*02 + 50*22 = 650 g.cm2
(b) Distance from y-axis will be x-coordinates
Iy = 20*(0)2 +30*(4)2 + 40*22 + 50*02 = 640 g.cm2
(c) distance from z-axis will be (x2+y2) where x & y denotes respective coordinates
Iz = 20*(32+02) + 30*(42+32) + 40*(22+0) + 50*(0 +22)
=> Iz = 1290 g.cm2
(d) d. A+B
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