http://s11.postimg.org/myh42cxer/GIANCOLI_ch08_p31.jpg Part A Calculate the mome

Question

http://s11.postimg.org/myh42cxer/GIANCOLI_ch08_p31.jpg

Part A

Calculate the moment of inertia of the array of point objects shown in the figure(Figure 1) about the vertical axis. Assume m = 2.0kg , M = 3.7kg , 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.

Express your answer using two significant figures.

Part B

Calculate the moment of inertia of the array of point objects about the horizontal axis.

Express your answer using two significant figures.

Part C

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

Explanation / Answer

Here ,

m = 2 kg

M = 3.7 Kg

Now , moment of inertia due to a mass , r distance from axis given as

I = m*r^2

A)

Here , about the vertical axis ,

moment of inertia . Iv = (m+M)*0.50^2 + (m+M)*1^2

Iv = (2+3.7)* 0.5^2 + (2 + 3.7)

Iv = 7.13 Kg.m/s^2

the moment of inertia about the vertical axis is 7.13 Kg.m/s^2

B)

about the horizontal axis

Ih = 2m * (0.5/2)^2 + 2M*(0.5/2)^2

Ih = 2 * 2 * (0.25)^2 + 2 * 3.7 * (0.25)^2

Ih = 0.713 Kg.m^2

the moment of inertia about horizontal axis is 0.713 Kg.m^2

c)

as moment of inertia is larger for vertical axis ,

it is harder to rotate about the vertical axis

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