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I have a top of unknown mass that has a moment of inertia $I=4\times 10^{-7} kg \cdot m^2$. A string is wrapped around the top and pulls it so that its tension is kept at 5.57 N for a distance of .8 m.

Could somebody help me derive some equations to help with this? Or to get me in the right direction? I have been trying to derive some sort of equations from $E=\frac{I \cdot \omega ^{2}}{2}$ but I cant get anywhere without ending up at radius = radius or mass = mass.

I need the final angular velocity.

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closed as off-topic by tpg2114, Qmechanic Nov 3 '13 at 2:26

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So far you haven't asked a question. What are you trying to find? The kinetic energy of rotation? Torque = moment-of-inertia * angular-acceleration will give you the final angular velocity ('course you'll need to know the radius of the wrapping...). Can you find the energy from there? –  dmckee Feb 2 '11 at 23:02
    
Sorry I changed it to include what I need. Can I equate the pulling force to the rotational energy? 1/2 I W^2 –  Justin Meiners Feb 2 '11 at 23:06
    
Justin: No. The units are wrong. You can equate the work (units of energy, right?) done in spinning the top with the energy of rotation. –  dmckee Feb 2 '11 at 23:08
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So could I use that Force * distance of the string and that would be energy? –  Justin Meiners Feb 2 '11 at 23:10
    
Try asking this at Yahoo questions where you will get some good answers. –  John McVirgo Feb 2 '11 at 23:17

2 Answers 2

You should be able to calculate the work done by pulling the string.

You should also be able to write down an equation for the amount of work necessary to accelerate an object with a given MOI to some arbitrary angular velocity.

That should be a good start.

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This question and ones like it are trying to get at the 'transferability' of energy between different frames of reference. You begin in a linear domain and move to a rotational domain. Whether you are considering the problem in the linear or rotational sense the inherent physics remains the same (at least in elementary examples such as this.), and so you can transfer physical quantities from one to the other.

The point I learned was that it helps to select a regime in which it is easy to calculate some figure of merit and which can be transfered simply to a regime in which the answer exists.

Energy is often useful in this case as it is scalar and invariant in the transform.

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Justin Meiners was seen last here on 2nd of February! –  Georg Apr 4 '11 at 10:42
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True but I thought this site was intended as a longer term resource? The answer is relevant to the whole class of questions. –  Nic Apr 4 '11 at 11:08

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