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Hey im so confused about moment of inertia. please help? 
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#1
Apr2912, 07:43 PM

P: 11

I=mr^2 I know moment of inertia depends on how for a object how far a bit of mass of that object is from the axis of rotation. i.e. farther from the axis = higher moment of inertia= more torque is needed to cause rotation. this just doesnt make any sense for the seesaw example, on the seesaw the farther the object is from the axis of rotation, the LESS torque you actually need. (you need more torque closer to the pivot) this e.g. just contradicts my first sentence.
can you please help i've been confused on this for quite awhile... 


#2
Apr2912, 10:44 PM

P: 452

Torque is not something that is "needed to cause rotation". Torque is the rate of change of angular momentum and a good way to think about is, is like you do about forces. The second law is F=ma similarly T=lα where α is the angular acceleration. When you apply a force F, on two different masses , the acceleration of the smaller mass will be higher. In the same way if you have two object of different moments of inertia and you apply the same torque the angular acceleration of the smaller l will be higher.So in the case of the seesaw if you want to have the same angular acceleration for a mass close to the pivot and one far. You will need a higher torque for the far mass and a smaller torque for the close one.



#3
Apr2912, 11:18 PM

P: 1,874

Moment of inertia is telling you how your mass is distributed throughout your object (it literally is a moment), and, therefore, how angular momentum and energy act on it.



#4
Apr2912, 11:24 PM

P: 84

Hey im so confused about moment of inertia. please help?
A good way to think about this (given by Richard Feynman) is to think about a door, partly open. With one finger try to close it by pressing hard near the hinge edge  almost impossible. Now apply the same force near the edge away from the henge  easy.



#5
Apr3012, 08:44 AM

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#6
Apr3012, 09:01 AM

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I should say that an example to introduce the idea of MI would be to think of a mass on a light pole. The pole is on a bearing at one end and the position of the mass on the pole is adjustable. If you were to push at a point near the pivot, you would find that the angular acceleration of the massonpole would be much greater when the mass is near the pivot than it would be at the end  for a given force. The angular acceleration for a given force (at a given position) is inversely proportional to the square of the distance of the mass from the pivot. The MI is Mx^{2}, where x is the distance from the pivot. For a set of masses (or a large object with distributed mass) you just add up all the masses times their x^{2}s to give the total Moment of inertia. The MI formula happens to be just the same as the Standard deviation of a statistical distribution  which used sometimes to be referred to as the second moment of a distribution. 


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