A gyroscope consists of a spinning wheel mounted inside a support structure (Figure P12.89). Because of conservation of angular momentum, the gyroscope keeps its orientation in space unless some outside force causes a torque on it. Suppose the \(1.0-\mathrm{kg}\) spinning wheel of a certain gyroscope has a diameter of \(0.10 \mathrm{~m}\) and is spinning at 14,200 revolutions per minute. What is the magnitude of the torque required to tilt the gyroscope \(90^{\circ}\) in \(20 \mathrm{~s}\) such that the spin speed is still 14,200 revolutions per minute when the gyroscope is in its new orientation?

Data from Figure P12.89

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1.0 kg 0.10 m