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Factors Which Determine the Moment of Inertia of a Body
Since mass is a measure of the inertia of a body we might reasonably expect the moment of inertia of a body to depend on the mass.  
   
For example, imagine two flywheels like the one shown here, one made of aluminium (density about 2700kgm-3) and the other of lead, density about 11300kgm-3).  
(A "flywheel" is just a wheel but usually quite a massive one, used for storing energy by virtue of its rotation.)  
Which one would be harder to speed up or slow down?  
The answer is obvious.  
   
Experiments show that, if we compare bodies of similar shape and size but having different masses, the moment of inertia, I is directly proportional to the mass.  
(This also assumes we are rotating the bodies around the same axis.)  
   
   
Now consider a flywheel like the one shown here.  
Imagine that it has the same total mass as the one above.  
   
It is clear that here the mass is much further away from the axle than before.  
   
This means that, for a given angular speed, ω, the linear speed of the particles of which the wheel is made is much greater (so they possess more kinetic energy).  
   
Therefore, to accelerate the wheel from zero to ω would require more work to be done and so we reasonably would expect greater forces and/or torques to be needed.  
   
We conclude that this wheel has a greater moment of inertia the the previous one.  
   
In conclusion:  
The moment of inertia of a body is directly proportional to its mass and increases as the mass is moved further from the axis of rotation.  
   
You can convince yourself of the second part of the conclusion next time you buy something heavy (massive) in a supermarket, eg a pack of water bottles (or, maybe more interestingly, beer or wine bottles).  
Place the massive packs near to yourself in the supermarket trolley... no problem when turning to avoid a collision with another trolley...  
   
Now try putting the pack at the front end of the trolley, furthest from you... you will find the risk of collisions much greater!  
   
N.B.  
The fact that I depends on mass distribution means that the same body can have different moments of inertia depending on which axis of rotation we consider.  
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