Question

What is the total moment of inertia of a system of several objects rotating together

Answer 1

Answer:

Lets take

Point mass of objects are m₁ ,m₂ ,m₃ ---and so on

The distance from axis of rotation is r₁ ,r₂ ,r₃ ----and so on  

We know that moment of inertia I  given as

I=∫dm .r²  kg.m²  

I = m₁ r₁² +m₂r₂²+m₃r₃² ------------- kg.m²  

Note-

1 .For point mass

 I=  m r²

2.For disk

$I=\dfrac{mr^2}{2}$

3. For circular ring

 I=  m r²

4. For rod length of L

$I=\dfrac{mL^2}{12}$

If all the objects are rotating together then the total moment of inertia will be summation of the moment of inertia of the all objects

I(total) = I₁ +I₂ +I₃+ ------kg.m²