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An object of mass m is on a frictionless table rotating with a given tangential speed vo with a radius of string ri. The string goes down through a hole (no friction) in the table where a given applied force, FA pulls down on the string a given distance d. Then, the object still keeps rotating but in a smaller and smaller circle. Find the final speed of the object after the rope was pulled down the distance d.
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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