Calculating moments of intertia

[Linus Pauling]

1. Find the moment of inertia I_x of particle a with respect to the x-axis (that is, if the x-axis is the axis of rotation), the moment of inertia I_y of particle a with respect to the y axis, and the moment of inertia I_z of particle a with respect to the z axis (the axis that passes through the origin perpendicular to both the x and y axes).

Particle a is located at x=3r, y=r, z=o



2. I = Integral(x^2 + y^2)



3. I_x = 1/3 * mr^3
I_y = 3mr^3
I_z = 10/3 * mr^3

 

[Delphi51]

Surely the formula is I = m*r^2 ?
so I_x = mr^2.
No integration needed when you have a point charge. The particle is a distance r from the x-axis. Your r^3 answers don't even have the right units.

 

[Linus Pauling]

Ah, ok thanks. Now I am supposed to consider a second particle, b, located at x=r and y=-4r, and calculate the total moment of inertia for the two particles of this system, with the y-axis as the axis of rotation.

Why 10mr^2 not the answer? I obtain this my summing I_ya + I_yb = 9mr^2 + mr^2

 

[Linus Pauling]

This is is driving me crazy

 

[Delphi51]

10mr^2 looks good to me, assuming the two particles have the same mass.