What is exactly the moment of inertia all about? Clueless~

Question

anonymous · Answer

it has a lot of formulas depending on the shape isnt it?

anonymous · Answer

itis the rotational analogue of mass.yeah there are.u can find out by using parallel axis theorems and perpendicular axis theorem!!

anonymous · Answer

i dont understand this question. Four particles A, B, C and D of mass 2 kg, 5 kg, 6 kg and 3 kg respectively are rigidly joined together by light rods to form a rectangle ABCD where AB=2a and BC=4a. Find the moment of inertia of this system of particles about an axis along AB..

anonymous · Answer

do i have to use I=Md$$^{2}$$

mani_jha · Answer

I had the exact same question in my mind when I started rotation. Unfortunately, none of my teachers could explain it that thouroughly. I had to do some self-research. :)
You know what is inertia, right? A more massive mass requires more force to be moved. Mass is a measure of inertia. Now, when something rotates about its axis, the amount of force required to stop it does not depend only on the mass, but also a new thing - The distance from the axis. 
Try it. Try to move a stationary fan by giving it a strike it at its edge. It easily rotates. Then try to strike it somewhere near the center. It moves less. You have to apply more force to move something closer to the axis of rotation. So, now, the inertia of a rotating object is not only a function of mass, but also of the distance from the axis of rotation.
You can try to find the kinetic energy of a rotating particle. Considering angular velocity for v, you will find the kinetic energy to be:
$$mr ^{2} w ^{2}/2$$.
The linear kinetic energy is
$$mv ^{2}/2$$
Compare these, and you will find that during rotation, the mass of a body is equivalent to mr^2. This new quantity is known as moment of inertia(you can clearly see moment of inertia increases with increasing distance from the axis)
Did u get this?

anonymous · Answer

Yeah! Great explanation.. I can finally picture it in my head.. :D bout my question i have to make the line of axis parallel to AB.. rite??

mani_jha · Answer

Yes, right. First find the moment of inertia about the centre of the system. Then use the parallel axis theorem(do u know it?)

anonymous · Answer

about the centre??

anonymous · Answer

so d=2a rite?? if from centre..

anonymous · Answer

sorry.. im a bit slow..

mani_jha · Answer

Wait, you can do without the parallel axis theorem. The axis is AB. Take the coordinate axis along AB(x or y). Then find the distance of the four masses from the origin. Find the moment of inertia of each, and add them up.
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I have considered A as the origin. Use the distance formula to calculate the distance of each mass from origin, and then use I=mr^2.