Calculating Moment of Inertia for a Physical Pendulum

[sajama]

Hi,

Would appreciate any help anyone has for me.

I am building a physical pendulum of sort, which consists of a hollow cylinder, which I am going to fill with sand. I am going to let the sand flow out of the pendulum and investigate the change in period with changing mass.

I also am mathematically/computationally modelling this. I am currently trying to figure out the equations of motion that I'm going to need to model this. I know the equation for the period of a physical pendulum is T=2*pi*sqrt(I/mgh), where h will be changing at a constant rate.
I'm wondering how to calculate the moment of inertia. I've found equations on hyperphysics for common moments of inertia (http://hyperphysics.phy-astr.gsu.edu/HBASE/mi.html#) but as my pendulum is going to be partly a solid cylinder and partly a hollow one, I'm not sure how to merge these equations. Has anyone got any advice?

Thanks in advance :)

 

[tiny-tim]

… I'm wondering how to calculate the moment of inertia. I've found equations on hyperphysics for common moments of inertia (http://hyperphysics.phy-astr.gsu.edu/HBASE/mi.html#) but as my pendulum is going to be partly a solid cylinder and partly a hollow one, I'm not sure how to merge these equations. Has anyone got any advice?

Hi sajama!

moment of inertia is additive …

so just add the moments of inertia of the two cylinders as if they were completely separate.

And of course, you'll also need the parallel axis theorem, since your moment of inertia is not about the centre of mass.

(btw, there's a better list at http://en.wikipedia.org/wiki/List_of_moments_of_inertia" … and you need to learn all of them )

 

[I_am_learning]

You can just algebraically add moment of inertia of various bodies if they have the same axis of rotation.