A) Calculate the moment of inertia of the array of point objects shown in the fi

Question

A) Calculate the moment of inertia of the array of point objects shown in the figure (Figure 1)about the vertical axis. Assume m = 2.3kg , M = 3.0kg , and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.

Iy= _______________ kg?m2

B)Calculate the moment of inertia of the array of point objects shown in the figure about the horizontal axis. Assume m = 2.3kg , M = 3.0kg , and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.
Iy= _______________ kg?m2

C) About which axis would it be harder to accelerate this array?

x or y ?

  

A) Calculate the moment of inertia of the array of point objects shown in the figure (Figure 1)about the vertical axis. Assume m = 2.3kg , M = 3.0kg , and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis. Iy= _______________ kg?m2 B)Calculate the moment of inertia of the array of point objects shown in the figure about the horizontal axis. Assume m = 2.3kg , M = 3.0kg , and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis. Iy= _______________ kg?m2 C) About which axis would it be harder to accelerate this array? x or y ?

Explanation / Answer

Note that

I = Sum(mi ri^2)

where mi = the ith mass

ri = the distance of the ith mass from the axis

Thus,

I = 13.3 kg*m^2   [ANSWER, PART A]

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Using the same equation,

I = 0.663 kg*m^2    [ANSWER, PART B]

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Greater I is harder to accelerate, as alpha = Torque/I.

Thus, it is harder to accelerate this through the VERTICAL AXIS. [ANSWER]

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