What is the Moment of Inertia for a Non-Uniform Cane with Attached Device?

[UKDv12]

I have a cane with non-uniform density and I'm trying to find its moment of inertia. There is no equation for its mass/density vs. length. If you need to picture it, it's a folding White Cane used by the blind. https://www.amazon.com/dp/B000VB0CG0/?tag=pfamazon01-20

I found the center of mass in a crude way by just trying to balance it. The axis of rotation should be about 12 cm down from the handle, or 126.5 cm from the bottom, since this is where it is often held. I was wondering if anyone could help me find its moment of inertia at this axis.

Cane Length: 138.5 cm
Center of Mass: 63.5 cm from the handle, 75 cm from the bottom
Cane Weight: 255.15 grams

I am also trying to find the moment of inertia when a device weighing 230 grams is attached 30 cm from the top of the cane. The center of mass of the entire apparatus when the device is added is 50 cm from the handle of the cane and 88.5 from the bottom.

 

[Curl]

That information is not sufficient in determining the inertia. What you can do is swing it like a pendulum and find the frequency of oscillation, then you can calculate the inertia.

 

[UKDv12]

Sorry, I don't quite follow. I'm confused on how I calculate moment of inertia from frequency.

 

[Curl]

I'm positive you learned this in intro physics class but you don't recall. Here's a refresher:

http://en.wikipedia.org/wiki/Pendulum#Compound_pendulum

 

[UKDv12]

I've taken a look at that, but I don't understand why the radius of gyration is different from the distance from the pivot to the center of mass.

 

[Curl]

Because points farther away from the rotation pivot move faster. Now you're getting into low level physics, i.e. asking why we define inertia of a particle as mr^2 etc.