The masses and coordinates of four particles are as follows: 45 g , x = 1.0 cm ,

Question

The masses and coordinates of four particles are as follows: 45 g, x = 1.0 cm, y = 1.0 cm; 30 g, x = 0.0 cm, y = 4.0 cm; 20 g, x = -3.0 cm, y = -3.0 cm, 50 g, x = -1.0cm, y = 3.0 cm. What is the rotational inertia of this collection with aspect to the x-axis ( kg m2)?

What is the rotational inertia of this collection with aspect to the y-axis?

What is the rotational inertia of this collection with aspect to the z-axis?

Please answer this right I've asked this twice on chegg and the answers have been wrong so far

Explanation / Answer

the total moment of inertia for a rigid body consisting of N point masses Mi with distances Ri to the rotation axis equals the sum of the point-mass moments of inertia

I = Sum (Mi*Ri^2)

with aspect to x axis

Ri = distance from x axis = y cordinates

I = 45*1^2 + 30*4^2 + 20*3^2 + 50*3^2 = 1155 g.cm^2 = 1.155*10^(-4) kg.m^2

with aspect to y axis

I = 45*1^2 + 30*0^2 + 20*3^2 + 50*1^2 = 275 g.cm^2 = 0.275*10^(-4) kg.m^2

with aspect to z axis

I = 45*(1^2 + 1^2) + 30*(0^2 + 4^2) + 20*(3^2 + 3^2) + 50*(1^2 + 3^2) = 1430 g.cm^2 = 1.430*10^(-4) kg.m^2

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