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Finding Moment of Interia of a 'Loop' when given Density & Cross sectional area...

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Jul28-11, 03:43 PM
P: 1
1. The problem statement, all variables and given/known data

I eventually have to solve for maximum angular acceleration of the loop in a magnetic field, and I have gotten everything with the exception of the moment of inertia, so I won't include the emf and B known variables.
Known: a copper wire with a density of [itex]\rho[/itex] = 8960 kg/m3 is formed into a circular loop of radius 0.50 m. Cross sectional area of the wire is 1.00 x 10-5m2.

2. Relevant equations
(and eventually) [itex]\tau[/itex] = [itex]\alpha[/itex]I

3. The attempt at a solution
I know since mass isn't given, I need to integrate something so I can use the density. However, it's been a really long time since I've integrated, so I'm not very familar with it. I've been unable to find an equation to find the volume of the 'loop,' so I know integration is the only way.
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Mike Pemulis
Jul28-11, 04:10 PM
P: 120
No integration required. A loop is just a cylinder bent into a circle. Imagine bending the loop back into a "normal" cylinder, and find the volume of that object. (If you don't remember the formula for the volume if a cylinder, it is easy to find).
Jul28-11, 04:12 PM
P: 140
You can approximate the loop as a circle (line) because the cross section is much smaller than the radius.

Mike Pemulis
Jul29-11, 10:23 AM
P: 120
Finding Moment of Interia of a 'Loop' when given Density & Cross sectional area...

Yes, I forgot to add that part. But first, OP needs to find the mass, which requires finding the volume.

Once that is done you would forget about the finite width and simply use I = MR2

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