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how do we calculate the moment of inertia of a solid cone?

how do we calculate the moment of inertia of a solid cone?

Grade:11

1 Answers

Askiitian.Expert Rajat
24 Points
12 years ago

Hi Deepak,

 

Divide the Cone into Infinitesimal Discs as shown in the figure

 

4809-636_6001_untitled.JPG

Now calculate the Moment of Inertia of this disc using sdn as the nass and a proportional radius of t6his disc of infinitesimal thickness found using similar triangles

Then integrate using

the following formula

I = ∫r2dm

In this case r would be varying and so you have to determine dm in terms of r and dr

Then integrate over the whole cone

 

Regards

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