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Zolol [24]
3 years ago
6

A 2.00 kg mass is located at (4.00 m, 0.00 m, 0.00 m) and a 4.00 kg mass is located at (0.00 m, 3.00 m, 0.00 m). If this system

of masses rotated about the Z-axis perpendicular to the X-Y plane, then the moment of inertia of this system is:_______
Physics
1 answer:
Eduardwww [97]3 years ago
5 0

Answer:

The moment of inertia of this system is 68 kilogram-square meters.

Explanation:

We have two particles rotating about the z-axis, which is orthogonal to xy plane, the moment of inertia of the system (I_{z}), measured in kilogram-square meters, is determined by the following formula:

I_{z} = \Sigma \limits_{i=1}^{2}m_{i}\cdot r_{i} (1)

Where:

m_{i} - Mass of the i-th particle, measured in kilograms.

r_{i} - Distance of the i-th particle from axis of rotation, measured in meters.

By Pythagorean Theorem we calculate each distance:

(x_{1}, y_{1}, z_{1}) = (4\,m, 0\,m,0\,m)

r_{1}=\sqrt{(4\,m-0\,m)^{2}+(0\,m-0\,m)^{2}+(0\,m-0\,m)^{2}}

r_{1} = 4\,m

(x_{2},y_{2}, z_{2}) = (0\,m, 3\,m, 0\,m)

r_{2} = \sqrt{(0\,m-0\,m)^{2}+(3\,m-0\,m)^{2}+(0\,m-0\,m)^{2}}

r_{2} = 3\,m

If we know that m_{1} = 2\,kg, r_{1} = 4\,m, m_{2} = 4\,kg and r_{2} = 3\,m, then the moment of inertia of the system is:

I_{z} = m_{1}\cdot r_{1}^{2}+m_{2}\cdot r_{2}^{2} (1b)

I_{z} = (2\,kg)\cdot (4\,m)^{2}+(4\,kg)\cdot (3\,m)^{2}

I_{z} = 68\,kg\cdot m^{2}

The moment of inertia of this system is 68 kilogram-square meters.

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