Question

What is the moment of inertia of a pendulum with a mass of `8 kg` that is `1 m` from the pivot?

Answer 1

`I=8color(white)(l)"kg"*"m"^2`

Explanation:

Taking the pendulum bulb as a point mass and the pivot as the rotational axis,

`m_"bulb"=8color(white)(l)"kg"`
`r=1color(white)(l)"m"`

Moment of inertia of the bulb as a point mass: [1]

`I=m*r^2=8color(white)(l)"kg"*"m"^2`

Note that the momentum of inertia expression can be derived using the parallel axis theorem: [2]

`I=I_"cm"+m*d^2`

Where `I_"cm"=0` for a point mass and `d=r` the axis of rotation distance from the axis passing through the center of mass.

Hence `I=m*d^2=m*r^2`
Reference
[1] List of moments of inertia, the English Wikipedia, https://en.wikipedia.org/wiki/List_of_moments_of_inertia
[2] Parallel axis theorem, the English Wikipedia, https://en.wikipedia.org/wiki/Parallel_axis_theorem