A wheel is rotating freely at angular speed 550 rev/min on a shaft whose rotational inertia is negligible. A second wheel, initially at rest and with 3 times the rotational inertia of the first, is suddenly coupled to the same shaft. (a) What is the angular speed of the resultant combination of the shaft and two wheels? (b) What fraction of the original rotational kinetic energy is lost?
(a) the Answer is 14.39 rad/sec
(b) ?
(a) the Answer is 14.39 rad/sec
(b) ?
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b) MI has increased by factor 4, but "w" has decreased by factor 4.
In energy, , because w is squared, this means a decrease factor of 16. With the increase of 4 from the MI, that leaves the overall decrease to be a factor of 4
The Ke (rot) decreases by 75%
3/4 of the original KE (rot ) is "lost"
In energy, , because w is squared, this means a decrease factor of 16. With the increase of 4 from the MI, that leaves the overall decrease to be a factor of 4
The Ke (rot) decreases by 75%
3/4 of the original KE (rot ) is "lost"