Rotation due to a magnetic field

AI Thread Summary
A uniform rectangular coil with a mass of 270 kg and dimensions of 0.5 m by 0.1 m is placed in a 4.00-T magnetic field, and a current of 2.90 A is applied. The discussion centers on calculating the angular acceleration using the formula that relates torque to moment of inertia. The main challenge is determining the moment of inertia for the coil, as the user is uncertain about the mass distribution. There is a request for assistance in solving this problem, particularly in visualizing the necessary calculations. Understanding the moment of inertia is crucial for solving the angular acceleration in this context.
dpeagler
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Homework Statement



A uniform rectangular coil of total mass 270 and dimensions .5 m x .1 m is oriented perpendicular to a uniform 4.00-T magnetic field (the figure ). A current of 2.90 A is suddenly started in the coil.

Homework Equations



angular acceleration = torgue / moment of inertia

The Attempt at a Solution



I really don't know what to do on this one, simply because I don't know what to do for the moment of inertia term. I thought about breaking it up into the moment of inertia of the base and height sides, but I don't know how the mass is distributed so I can't do that.

If anyone can help that would be great.
 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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