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# Moment of inertia of some ice cream watch

1. The diagram I drew for this is just an ice cream cone shape with vertex on O and as the axis of symmetry.

Initially I thought of combining the two in such a way that the inertia is given by:

where are spaces occupied by the cone and hemisphere respectively, but this seems like a nightmare to deal with.

Having looked at the reference answer of I thought that you'd just add the inertia's from the two separate objects since inertia of the cone about the same axis is , however the inertia of the hemisphere worked out to be instead.

Is there a shortcut to this problem? Is addition of inertia's in these types of problems allowed, so the ref-answer answer is incorrect?

For inertia of the hemisphere I just evaluate which yields it, but I can't see where I'd be going wrong here.
2. (Original post by RDKGames)
For intertia of the hemisphere I just evaluate which yields it, but I can't see where I'd be going wrong here.
MofI of the hemisphere should be

And yes they are additive.

Edit: Looks as if you slipped a factor of 2 in that intergral soimewhere.
3. (Original post by ghostwalker)
MofI of the hemisphere should be

And yes they are additive.
Hm.. not sure where I'm tripping up then

4. (Original post by RDKGames)
Hm.. not sure where I'm tripping up then

Not well up on 3D coordinate change of variables, but shouldn't the second line be:

5. (Original post by ghostwalker)
Not well up on 3D coordinate change of variables, but shouldn't the second line be:

Don't think so (although using that does indeed yield 1/5 as required)

The relation I'm given is for , and , as well as being told that

Spoiler:
Show

6. (Original post by RDKGames)
Don't think so (although using that does indeed yield 1/5 as required)
Fair enough. I wasn't sure which version of spherical you were using.

Nope, can't see the problem.
7. (Original post by RDKGames)
...
Nope, I'm being stupid.

The MofI of the hemisphere is 2/5Ma^2, not 1/5.

I was working from the MofI of a sphere, and halving it, but forgot the mass is halved too, so the formula is the same. Doh!

8. (Original post by ghostwalker)
Nope, I'm being stupid.

The MofI of the hemisphere is 2/5Ma^2, not 1/5.

I was working from the MofI of a sphere, and halfing it, but forgot the mass is halved too, so the formula is the same. Doh!

So then my lecturer has indeed made a typo there with the reference answer?
9. (Original post by RDKGames)

So then my lecturer has indeed made a typo there with the reference answer?
I reckon so - they probably did the same thing I did.

Apologies for wasting your time.
10. (Original post by ghostwalker)
I reckon so - they probably did the same thing I did.

Apologies for wasting your time.
I'll drop 'em an email then. Thanks anyhow!
11. (Original post by RDKGames)
I'll drop 'em an email then. Thanks anyhow!
For confirmation:

See here.
12. (Original post by RDKGames)
I'll drop 'em an email then. Thanks anyhow!
In your email, I should drop the spare t from your work. It's moment of inertia, not moment of intertia.
13. (Original post by tiny hobbit)
In your email, I should drop the spare t from your work. It's moment of inertia, not moment of intertia.
Haha I didn't even notice including that!

Thankfully it was not written like that in the email
14. (Original post by RDKGames)

The diagram I drew for this is just an ice cream cone shape with vertex on O and as the axis of symmetry.

Initially I thought of combining the two in such a way that the inertia is given by:

where are spaces occupied by the cone and hemisphere respectively, but this seems like a nightmare to deal with.

Having looked at the reference answer of I thought that you'd just add the inertia's from the two separate objects since inertia of the cone about the same axis is , however the inertia of the hemisphere worked out to be instead.

Is there a shortcut to this problem? Is addition of inertia's in these types of problems allowed, so the ref-answer answer is incorrect?

For inertia of the hemisphere I just evaluate which yields it, but I can't see where I'd be going wrong here.
misleading post - thought it was about ice cream yet you only mention ice cream once!! poor keyword density pal

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