# I Finding Moment of Inertia of a wheel experimentally

1. Oct 2, 2016

### Loudhvx

Hello all, and forgive me if I'm making newbie mistakes as I haven't posted here much.

I realize this appears to be a homework assignment, but it is not. I am trying to develop an easy method for determining the actual moment of inertia for real wheels, for bicycles and other vehicles. I googled the topic and many related results came up, but not explicitly for finding the MOI with a simple formula.

I believe I have the correct formula, but I need confirmation from more knowledgeable people. I made a pdf file summarizing the problem including a drawing. I hope the link works.

https://s3.amazonaws.com/loudfiles/MomentOfInertiaWheel_TEMP.pdf

All of the quantities are constant, as in not varying with time.
I neglect friction, but realize it can be a significant factor on a real wheel if not dealt with properly.

In case the link doesn't work, here is what I have:
A wheel of radius R is mounted with its axle horizontal.
A string is attached, and wrapped around the perimeter of the wheel (at radius R distance from the center).
The free end of the string is attached to a free-weight of mass M.
The free weight is allowed to fall a distance H, vertically, which accelerates the wheel.
The time it takes the weight to travel H is time t1.
g is the acceleration of gravity.

The MOI = ( (g t12 / 2 H) - 1 ) M R2

Can someone please confirm that for me? Thank you very much for your time.

2. Oct 2, 2016

### Loudhvx

I forgot this can probably also be done using energy equations, so I forgive me, as that would have been a way I could check my results. If someone has that solution handy, that would be great as well. I will attempt that, but it will likely take me some time to brush up on those equations/concepts.

3. Oct 5, 2016

### CWatters

Perhaps see ...

4. Oct 6, 2016

### Loudhvx

Thanks. That does at least confirm the relationship of I to a.

5. Oct 8, 2016

### Staff: Mentor

You might be able to devise a way to take into account friction in your calculation of MOI.