Find the moment of inertia Ix of particle a with respect to the x axis (that is, if the x axis is the axis of rotation), the moment of inertia Iy of particle a with respect to the y axis, and the moment of inertia Iz of particle a with respect to the z axis (the axis that passes through the origin perpendicular to both the x and y axes). Express your answers in terms of m and r separated by commas. Ix, Iy, Iz =

The definition of moment of inertia allows to find the results for the moment of inertia with respect to each axis are:

   a) Iₓ = m r²

   b) = 9 m r²

   c) = 10 m r²

The moment of inertia is a scalar quantity is obtained by the expression

        I =∫ r² dm

Where I is the moment of inertia, m the mass of the body and r the distance from the axis of rotation.

In the case of point particles, the expression reduces to

     I = m r²

In this case we calculate with respect to each coordinate axis.

a) With respect to the x axis the distance is x = r, the moment of inertia is

       Iₓ = m r²

b) with respect to the y-axis, indicate that the distance is y = 3 r.

We calculate

         I_y = m (3r) ²

         I_y = 9 m r²

c) Regarding the z-axis.

We look for the distance.

          z =    

          z =  

We calculate the moment of inertia.

         Iz = m (10r²)

         Iz = 10 m r²

In conclusion using the definition of moment of inertia we can look for the results of the moment of inertia for each axis are:

   a) Iₓ = m r²

   b) I_y = 9 m r²

   c) I_z = 10 m r²

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In the problem the data of the distance to the x and y axis is incomplete, these data are distance to x-axis x = r and the distance to the y axis y= 3r.

Ix,Iy,Iz = mr²,9mr²,10mr²

Explanation:

The Question has some missing details.

To solve this question, I'll make the following assumptions.

Distance of particle x = r

Distance of particle y = 3r

Given

The mass of each particles = m

The moment of inertia is calculated by adding product of mass” of each particle with the “square of its distance from the axis of the rotation”.

Ix = m * (r)² = mr²

Iy = m(3r)² = m * 9r² = 9mr²

The distance of z from the axis is r² + (3r)²

So, Iz = m(r² + (3r)²)

Iz = m(r² + 9r²)

Iz = m(10r²)

Iz = 10mr²

So, we have

Ix,Iy,Iz = mr²,9mr²,10mr²

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