A rotating flywheel slows down at a constant rate due to friction in its bearings. After 1.00 min, its angular velocity has diminished to 0.928 of its initial value ω𝜔. At the end of the fifth minute what is the angular velocity in terms of the initial value? Do not enter unit.
Question
A rotating flywheel slows down at a constant rate due to friction in its bearings. After 1.00 min, its angular velocity has diminished to 0.928 of its initial value ω𝜔. At the end of the fifth minute what is the angular velocity in terms of the initial value? Do not enter unit.
Solution
To solve this problem, we need to understand that the flywheel is undergoing a constant angular deceleration. This means that the ratio of the final angular velocity to the initial angular velocity is the same for any given time interval.
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After 1 minute, the angular velocity is 0.928 of its initial value.
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Therefore, after 5 minutes, the angular velocity will be (0.928)^5 of its initial value.
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To calculate this, simply raise 0.928 to the power of 5.
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(0.928)^5 = 0.695
So, at the end of the fifth minute, the angular velocity is 0.695 times its initial value.
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