# What is the moment of inertia ia of particle a?

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 xand y axes).
Express your answers in terms of m and r separated by commas.

1)
The moment of inertia of particle is,

I=M R^{2}

The mass of particle a is m and the perpendicular distance of particle a from $x$ axis is T.

Substitute m for M and r for R.

The moment of inertia of particle a with respect to x axis is,

I_{x}=m r^{2}

The moment of inertia of particle a with respect to x axis, I_{x}, is m r^{2}.

2)

The moment of inertia of particle is,

I=M R^{2}

The mass of particle a is $m$ and the perpendicular distance of particle a from y axis is 3 r.

Substitute m for M and 3 r for R.

The moment of inertia of particle a with respect to y axis is,

I_{y}=m(3 r)^{2}

=9 \mathrm{mr}^{2}

The moment of inertia of particle a with respect to y axis, I_{y}, is 9 m r^{2}

3)

The moment of inertia of particle a with respect to z axis is,

I_{z}=I_{z}+I_{y}

Substitute m r^{2} for I_{x} and 9 m r^{2} for I_{y}.

The moment of inertia of the particle with respect to z axis is,

I_{z}=m r^{2}+9 m r^{2}

=10 m r^{2}

The moment of inertia of particle a with respect to z axis, I_{z}, is 10 \mathrm{mr}^{2}

### Raymond Puzio Raymond Puzio has a PhD in Physics from Yale University. I have been creating PlanetPhysics with Aaron Krowne and Ben Loftin since 2005.