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

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force