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The masses and coordinates of four particles are as follows: 25 g , x = 2.0 cm ,

ID: 2294443 • Letter: T

Question

The masses and coordinates of four particles are as follows: 25 g, x = 2.0 cm, y = 2.0 cm; 40 g, x = 0.0 cm, y = 4.0 cm; 40 g, x = -3.0 cm, y = -3.0 cm, 25 g, x = -3.0cm, 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?
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?

Explanation / Answer

with respect to X axis

momento f inertia of a mass = mr^2

r = distnace from the axis


MIx= .025*.02^2 + 40*.04^2 + 40*.03^2 + 25*.03^2 = 1.325 x 10^-4 kg.m^2


with respect to Y axis


MIy = .025*.02^2 + .04*0^2 + .04*.03^2 + .025*.03^2 = 6.85 x 10^-5 kg.m^2


with respect to z axis

r1 = sqrt(2^2 + 2^2) = sqrt(8) cm

r2 = 4 cm

r3 = sqrt(18) cm

r4 = sqrt(18) cm


MIz = .025*.0008 + .04*.0016 + .04*.0018 + .025*.0018 = 2.01 x 10^-4 kg.m^2