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A record with a 10 cm radius and 200 g mass is dropped vertically onto a freely rotating turntable (meaning the turntable is not being driven by a motor). Frictional forces act to bring the record and turntable to a common angular speed. The radius of the turntable is also 10 cm, and the mass is 2 kg. The initial angular velocity of the turntable is 5 rad/s. (i) What is the final angular velocity of the record and the turntable? (ii) If there is a net frictional torque of 0.1 N·m, how long will it take for the record and turntable to stop rotating?
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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