# Homework Help: Polar moment of inertia for a shaft with slot

1. Sep 1, 2010

### chaitac

1. The problem statement, all variables and given/known data
HI
Can anyone help me in finding out the polar moment of inertia of a hollow shaft with 3 circular slots . Its used in design of DIVERTERS in oil and gas application.

2. Relevant equations

3. The attempt at a solution

2. Sep 1, 2010

### rock.freak667

Do you have a diagram?

Do you know the dimensions of the slots? If you do, then you can just subtract the inertia of the slots from the inertia of the hollow shaft.

J= πd4/32

3. Sep 1, 2010

### chaitac

The slots are 1.031 long and 0.688 wide Like a Mill Slot . they are rounded at the end(Radius of the rounded ends 0.344). they are 3 slots at 120 degree apart place radially.

Thanks

4. Sep 1, 2010

### chaitac

I think the polar moment of inertia for a hollow shaft is J = π(D4-d4)/32 when derived from its center. I have the slots 0.250 distant from the end of the shaft. How does it change the MOI?

5. Sep 1, 2010

### rock.freak667

I think then, you can assume that they are like cylinders then, and just subtract them from the inertia of the entire thing. But I'm not too sure what a Mill Slot looks like so it is possible that I may suggesting the wrong thing.

6. Sep 1, 2010

### chaitac

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I hope you got how the slot is looking .

Last edited: Sep 1, 2010
7. Sep 1, 2010

8. Sep 1, 2010

### rock.freak667

Well in that case, I'd just approximate that shape to a cuboid.

Just find the inertia about its own center and then use the parallel axis theorem to find the inertia about the axis of the shaft.