In a Beams ultracentrifuge, the rotor is suspended magnetically in a vacuum. Sin

Question

In a Beams ultracentrifuge, the rotor is suspended magnetically in a vacuum. Since there is no mechanical connection to the rotor, the only friction is the air resistance due to the few air molecules in the vacuum. If the rotor is spinning with an angular speed of 5.1x105 rad/s and the driving force is turned off, its spinning slows down at an angular rate of 0.38 rad/s2.

(a) How long does the rotor spin before coming to rest?
(b) During this time, through how many revolutions does the rotor spin?

Explanation / Answer

Rotator spinning with an angular speed is  _0 = 5.1*10^5 rad /s Angular acceleration is = - 0.38 rad /s^2 a ) time taken to spin before comming to rest is      = _0 + t         = 5.1*10^5 rad /s +(- 0.38 rad /s^2 * t )     t = 13.4 *10^5 s b ) Number of revolutions is = _0 t + 1/2 t^2              = 5.1*10^5 rad /s * 13.4*10^5 s - 1/2 * 0.38 * (13.4*10^5 rad /s)^2              = 34.2*10^10 rad              = 34.2*10^10 rad /2              = 5.44*10^10 rev

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