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.

### Answer

**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}`