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37. Problem 12.53E (HRW) A wheel is rotating freely with an angular speed of 800 rev/min on a shaft whose rotational inertia is negligible. A second wheel, initially at rest and twice the rotational inertia of the first, is suddenly coupled to the same shaft. We have to find (a) the angular speed of the resultant combination of the shaft and the two wheels; (b) the fraction of the original rotational kinetic energy lost in the process. |
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Solution: Click For PDF Version Let the rotational inertia of the first wheel be I.
Its angular speed
When the second wheel of rotational inertia 2I, is coupled to the
shaft let the two wheels and the shaft rotate with angular speed
Rotational energy of the system when both wheels are attached with the shaft is
Fractional loss of rotational energy is
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Therefore, the angular momentum of the shaft and the wheel system is
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The initial rotational energy of the system is 
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From conservation of angular momentum, we find the changed angular speed
