How Can I Optimize the Moment of Inertia for an Out-of-Balance Load?

[Brad123]

Hello, I am trying to make something that spins out of balance. currently my current weighs are half circle in shape. I know that if I change the profile of the weights to a pie shape (less than 180deg semi circle) the center of mass moves away from the axis of rotation, but at the same time my mass is decreased (given same radius and thickness). Does anyone have the formulas that would help me optimize this? I am trying to reduce the overall radius of the spinning object for sizing and thought this might be the correct approach.
Thanks hopefully.

 

[jmatejka]

I think I see what you are saying, you want to "optimize the out of balance", obviously more weight over a less spread out area. Sounds like F=MA.

How about cutting your "pie" into many pieces, drill center holes into (each piece). Arrange the pieces as you wish(even stacking), then use a nut and bolt,(through all the center holes) to secure the pie pieces.

You could then physically vary your geometry. The smaller the slices, the more stacking, the greater the "out of balance".

 

[Brad123]

What I am trying to do is play with the balance of moving the center of gravity away from the rotational axis. The tradeoff is as you narrow the piece up the CM goes out, which increases your R. Problem is mass goes down at the same time, unless you stack or thicken it as you mention. The formulas I am using are V=(2piR)/T, T=period. radial Acceleration Arad=V^2/R and F=ma. I do not see much advantage so far in "narrowing up" the slice to increase R. With my period a constant and solving for radial acceleration in terms of R, and pluggin that into F=ma, neither m nor r are squared so they directly affect each other. Not sure, probably making this confusing. anyway I see no benifit to making the pie slice shape versus just a half circle.

 

[xxChrisxx]

You want to optimise the moment of inertia, other wise known as angular mass.

Bigger MOI = more out of balance.
You can apply any constraints you want to the geometry but MOI is your parameter to optimise.
Wiki it.