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Q. A spacecraft is in empty space. It carries on board a gyroscope with a moment of inertia of Ig = 23.0 kg · m2 about the axis of the gyroscope. The moment of inertia of the spacecraft around the same axis is Is = 5.00 105 kg · m2. Neither the spacecraft nor the gyroscope is originally rotating. The gyroscope can be powered up in a negligible period of time to an angular speed of 135 rad/s. If the orientation of the spacecraft is to be changed by 20.0°, for what time interval should the gyroscope be operated?
Q. Two weights are connected by a very light flexible cord that passes over a 30.0- frictionless pulley of radius 0.100 . The pulley is a solid uniform disk and is supported by a hook connected to the ceiling. One weight is 75.0 N and the other is 125 N.
What force does the ceiling exert on the block?
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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