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.
20 g x = -5.0 cm y = 0.0 cm
35 g x = 5.0 cm y = -4.0 cm
35 g x = -3.0 cm y = -3.0 cm
20 g x = 2.0 cm y = -5.0 cm

(a) What is the rotational inertia of this collection about the x axis?
____g·cm2

(b) What is the rotational inertia of this collection about the y axis?
_____g·cm2

(c) What is the rotational inertia of this collection about the z axis?
____g·cm2
(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)2
AB
A + B
A - B

Explanation / Answer

There was a problem with units last time. I am correcting it here.

rotational inertia =mr2 ,where m is the individual mass and r is the distance from the axis from which it is to be calculated

(a) Distance of any particle from x axis is its y coordinate.

mr2 = 20 x02 + 35 x 42 + 35x32 +20x52 =1375gcm2 ....(1)

(b) Distance of any particle from y axis is its x coordinate.

mr2 = 20 x52 + 35 x 52 + 35x32 +20x22 =1770gcm2 ....(2)

(c) Distance of any particle from z axis is the root of (sum of squares of x coordinate and y coordinate)

r =(x2+y2), r2= x2+y2 ...(3)

mr2 = 20 x(52+0) + 35 x (52+42) + 35x(32+32)+20x(22+52)=3145gcm2 ....(4)

(d) As we can clearly see from (1),(2),(3),(4) the answer is A + B

this result is easily obtained as perpendicular axis theorem

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