Physics: The masses and coordinates of four particles are as follows: 26 g, x = 3.0 cm, y = 3.0 cm; 18 g, x = 0, y = 6.0 cm; 15 g, x = -4.5 cm, y = -4.5 cm; 23 g, x = -3.0 cm, y = 6.0 cm. what are the rotational inertias of this collection about the (a) x, (b) y, and (c) z axes?

or any weather is the correct answer to this question...

The masses and coordinates of four particles are

hjeffrey168

02.01.2022

1) $I_{x}=2013.1gcm^{2}$

2) $I_{y}=744.75gcm^{2}$

3) $I_{z}=2747.85gcm^{2}$

Explanation:

Since the given masses are completely in xy plane we have

Moment of inertia about x axis equals

$I_{x}={\sum y_{i}^{2}m_{i}}$

Applying the values we get

$I_{x}={26\times 3^{2}+23\times 6^2+15\times (-4.5)^{2}+18\times 6^{2}}\\\\\therefore I_{x}=2013.1gcm^{2}$

Similarly

Moment of inertia about y axis equals

$I_{y}={\sum x_{i}^{2}m_{i}}$

Applying the values we get

$I_{x}={26\times 3^{2}+23\times (-3)^2+15\times (-4.5)^{2}+18\times 0^{2}}\\\\\therefore I_{y}=744.75gcm^{2}$

Now by theorem of perpendicular axis of moment of inertia we have

$I_{z}=I_{x}+I_{y}$

Appying values we get

$I_{z}=2013.1+744.75=2747.85gcm^{2}$

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