Three particles are connected by light rigid rods and arelocated in the x – y pl

Question

Three particles are connected by light rigid rods and arelocated in the x – y plane as follows. A 5.0 kg particleis located at x = - 5.0 m, y = - 5.0 m. A 3.0 kg particle islocated at x = + 3.0 m, y = + 4.0 m. A 4.0 kg particle islocated at x = - 4.0 m, y = 0. Calculate the moment ofinertia for this system of particles for: a.    Rotation about the x – axis.b.    Rotation about the y – axis. c.     Rotation about the z – axis. hoping someone can get me started in the right direction withthis one. I would really appreciate it. Thanks! a.    Rotation about the x – axis.b.    Rotation about the y – axis. c.     Rotation about the z – axis. hoping someone can get me started in the right direction withthis one. I would really appreciate it. Thanks! hoping someone can get me started in the right direction withthis one. I would really appreciate it. Thanks!

Explanation / Answer

I=mr^2 for a particle and the moment of intertia for the systemwill be the summation of the moments of all 3 particles. For a. around the x-axis you have m for all the particles and youneed r which will be the distance to the axis which is simply the yvalue of each particle so I=5(5)^2+3(4)^2+0 b. For around the y-axis r is the distance to the y-axis which isthe x value I=5(5)^2+3(3)^2+4(4)^2 c For around the z-axis you need to use the distance once more, butnow you need the distance formula I=5(5^2+5^2)+3(3^2+4^2)+4(4)^2

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