Why Do Moments Balance in a Faraday Disk but Not the Forces?

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In the discussion, a conductive disk rotates in a magnetic field while lifting a mass, prompting a calculation of current and angular velocity. The book suggests using the moment of forces to equate the weight force and magnetic force, leading to a specific relation for current. The question arises as to why the forces themselves cannot be equated directly, despite the moments being equal. Participants emphasize the need for a deeper understanding of the physics involved, particularly the distinction between moments and forces in this context. The conversation highlights the complexities of electromagnetic interactions and the importance of proper analytical approaches in solving such problems.
FabJohnson
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Hi to everybody! Please: can you help with this problem?
A conductive disk with a radius a = 20 cm, with negligible moment of inertia, rotates around its horizontal axis. The disc region around the radius is inserted in a magnetic field B = 0.75 T perpendicular to the disk itself. A mass is connected to the edge of the disc using a thin wire. The disk is connected to a circuit with an e generator. m. f. = 10 V. The overall resistance of the circuit is R = 0.3 Ohm. Under steady conditions, the disc rotates at an Omega angular velcoity, raising the mass. Calculate: a) the current of the regime that runs through the circuit and b) the angular velocity Omega.
My book calculates the current by the following relation:
mga=iB(a^2)/2 that is: the moment of weight force is equal to the moment of force obtained by the magnetic field. My question is: Why you can't establish the same relation between the forces?
I mean: mg=iBa. It's obviously another result, but I mean: why forces aren't equal, but the moments are?
 
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You will have to show us more of your work before our homework helpers will help.

Forget what the book says, how would you solve the problem?
 
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