Four point masses are arranged on the xy plane as follows. Mass1 = 45.0 grams at

Question

Four point masses are arranged on the xy plane as follows.

Mass1 = 45.0 grams at x = 2.00 cm and y = 2.00 cm.

Mass2 = 51.0 grams at x = 0.00 cm and y = 4.00 cm.

Mass3 = 27.0 grams at x = -3.00 cm and y = -3.00 cm.

Mass4 = 33.0 grams at x = -1.00 cm and y = 2.00 cm.

Part A:What is the rotational inertia if this collection of masses is rotating about the x axis?

Part B: What is the rotational inertia if this collection of masses is rotating about the y axis?

Part C: What is the rotational inertia if this collection of masses is rotating about the z axis?

Explanation / Answer

a.)I=sum of my^2

I = (0.045 * 002^2) + (0.051 * 0.04^2) + (0.027 * 0.03^2) + (0.033 * 0.02^2)

Ix = 0.180 kgm^2

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b.)I=sum of mx^2

Iy = (0.045 * 002^2) + (0.051 * 0^2) + (0.027 * 0.03^2) + (0.033 * 0.01^2)

I=0.180 Kgm^2

c.)I=sum of m*(x^2+y^2)

Iz = 0.045 * (0.02^2 + 0.02^2) + 0.051* (0.04^2) + 0.027 *( 0.03^2 + 0.03^2)
+ 0.033 * (0.01^2 + 0.02^2)

Iz = 0.0001827 kg m^2

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