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. 35 g x = 2.0 cm y = 3.0 cm 35 g x = 5.0 cm y = 5.0 cm 35 g x = -1.0 cm y = -4.0 cm 35 g x = 0.0 cm y = 4.0 cm (a) What is the rotational inertia of this collection about the x axis? (b) What is the rotational inertia of this collection about the y axis? (c) What is the rotational inertia of this collection about the z axis? (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?

Explanation / Answer

the rotational inertia of a particle with mass m = m*r^2, where r is the distance to the axis. so the rotational inertia of this collection about the x axis is m1*y1^2 + m2*y2^2 + m3*y3^2 = 35*(3.0)^2 + 35*(5)^2 + 35*(-4.0)^2 gcm^2 =1750 g cm^2 the rotational inertia of this collection about the y axis is m1*x1^2 + m2*x2^2 + m3*x3^2 = 35*(2.0)^2 + 35*(5.0)^2 + 35*(-1)^2gcm^2 =1050 gcm^2

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