Magnetostatics - Rotation of circular disc

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SUMMARY

The discussion focuses on calculating the time it takes for a rotating circular disc to slow to half its initial speed when a load is suddenly connected. The disc has a radius of 3 meters, a mass of 10^4 kg, and rotates at 3000 revolutions per minute in a magnetic field of 0.5 Tesla. The key equation derived for the electromotive force (emf) is w*a^2*B/2. The correct time to slow down to half speed is established as T=6.16 seconds, based on the relationship between kinetic energy loss and the electrical parameters of the circuit.

PREREQUISITES
  • Understanding of angular frequency and its relation to rotational motion
  • Familiarity with electromagnetic induction and emf calculations
  • Knowledge of kinetic energy equations for rotating bodies
  • Basic principles of electrical circuits, including resistance and power
NEXT STEPS
  • Study the derivation of the electromotive force in rotating systems
  • Learn about the conservation of energy in rotational dynamics
  • Explore the effects of magnetic fields on rotating conductive materials
  • Investigate the relationship between torque, angular momentum, and angular velocity
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Physics students, electrical engineers, and anyone interested in the dynamics of rotating systems and electromagnetic effects in conductive materials.

Keano16
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Homework Statement




A disc has radius a and rotates with angular frequency w. Magnetic flux density is B. Such a disc of mass 10^4 kg and radius 3m is rotating freely at 3000 revs/min in a field of 0.5T. A load of 10^-3 ohms is connected suddenly between the rim and the axis of the disc. How long would it take the disc to slow to half its initial speed?


Homework Equations





The Attempt at a Solution



I found an equation for the emf produced that is: w*a^2*B/2 . Using this I wanted to equate two equations -- kinetic energy of the rotating disc at half the intiial speed = (V^2/R)*T.

The answer is meant to be T=6.16s, but that's not what I have.

Thanks for any help.
 
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Keano16 said:
I found an equation for the emf produced that is: w*a^2*B/2 . Using this I wanted to equate two equations -- kinetic energy of the rotating disc at half the intiial speed = (V^2/R)*T.

No, the loss in kinetic energy should be equal to (V^2/R)*T.
 
Ah I see now -- thanks for your help!
 

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