Find the moment of inertia I_x, I_y, I_z of particle a with respect to the x, y, and z axis?

Question

Consider the system of two particles, a and b, shown in the figure

http://session.masteringphysics.com/problemAsset/1003163/29/134726A.jpg

Particle a has mass m, and particle b has mass 2m.

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).

Express your answers in terms of m and r separated by commas.

Answer 1

Ix = mr^2

Iy = m(3r)^2

Iz = m(r^2 + (3r)^2)