Yatayyat
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#1
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Question link: https://isaacphysics.org/questions/2part_moi

How would I do this problem?

I'm so confused on what exactly I need to do to find the moment of inertia of both point masses

This is what I have seen and tried but I can't see how it would help to get the answer?

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Thanks
Last edited by Yatayyat; 1 year ago
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the bear
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so i called x1 a and x2 b

a + b = L

M1a = M2 b

M1( L - b ) = M2 b

this can be rearranged to make b the subject.... *****


total moment of inertia of the rotating masses = M1a2 + M2 b2

replace M1 with M2 b/ a

and you get M2 ba + M2 bb

or M2 b( a + b )

which is M2 bL

now just replace b with the expression you found earlier *****
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Physics Enemy
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(Original post by Yatayyat)
...
CoM = Lm2/(m1 + m2) (set m1 at x = 0)

I1 = m1[Lm2/(m1 + m2)]^2
I2 = m2[L - Lm2/(m1 + m2)]^2
= m2[Lm1/(m1 + m2)]^2

I = I1 + I2 = m1m2[L/(m1 + m2)]^2(m2 + m1)
= [m1m2/(m1 + m2)]L^2
Last edited by Physics Enemy; 1 year ago
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Yatayyat
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(Original post by the bear)
so i called x1 a and x2 b

a + b = L

M1a = M2 b

M1( L - b ) = M2 b

this can be rearranged to make b the subject.... *****


total moment of inertia of the rotating masses = M1a2 + M2 b2

replace M1 with M2 b/ a

and you get M2 ba + M2 bb

or M2 b( a + b )

which is M2 bL

now just replace b with the expression you found earlier *****
I have tried this and followed your steps and got this

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Which does give me the right answer so thank you!
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Yatayyat
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(Original post by Physics Enemy)
CoM = Lm2/(m1 + m2) (set m1 at x = 0)

I1 = m1[Lm2/(m1 + m2)]^2
I2 = m2[L - Lm2/(m1 + m2)]^2
= m2[Lm1/(m1 + m2)]^2

I = I1 + I2 = m1m2[L/(m1 + m2)]^2(m2 + m1)
= [m1m2/(m1 + m2)]L^2
I have done this and written all the steps out again

It makes sense to me but where is the axis of rotation being used at when the point masses rotate? Is it at the given CoM or at one of the ends that we assign?

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Physics Enemy
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(Original post by Yatayyat)
It makes sense to me but where is the axis of rotation being used at when the point masses rotate? Is it at the given CoM or at one of the ends that we assign?
They both rotate about the system CoM. Rotation axis is the vert (z) axis through CoM, with masses rotating on an x-y plane. Hence we use distances to the CoM.
Last edited by Physics Enemy; 1 year ago
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Yatayyat
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(Original post by Physics Enemy)
They both rotate about the system CoM. Rotation axis is the vert (z) axis through CoM, with masses rotating on an x-y plane. Hence we use distances to the CoM.
Thank you I got it now
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