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Wire is often delivered wrapped on a large cylindrical spool. Suppose such a spool is supported by resting on a horizontal metal rod that is pushed through a hole that runs through the center of the spool. A worker is pulling some wire off the spool by exerting a force on it, as shown in the figure. Suppose the spool rotates on the rod essentially without friction. The spool is approximately a uniform cylinder with a mass of 50 kg and a radius of 30 cm. The worker pulls on the wire for 2 seconds with a force of 30 N. At the end of the 2 seconds, she immediately clamps on a brake which very quickly stops the spool’s rotation. Just before she put on the brake, how fast was the spool rotating? How much wire did she pull off the spool?
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
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