In a Beams ultracentrifuge, a 19.5 cm long rotor is suspended magnetically in a

Question

In a Beams ultracentrifuge, a 19.5 cm long 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 4.8 105 rad/s and the driving force is turned off, its spinning slows down at an angular rate of 0.39 rad/s2.
(a) For a point at the end of the rotor, find the initial speed.
answer is 0.936 e5 m/s

(b) For a point at the end of the rotor, find the tangential acceleration component.
answer is 0.0761 m/s2

(c) For a point at the end of the rotor, find the maximum radial acceleration component.
answer is 4.49e+10m/s2

Explanation / Answer

Length of the rotor is L = 19.5 cm = 0.195 m Initial angular velcoity is 1 = 4.8x105 rad/s Angular acceleration is = 0.39 rad/s2 ---------------------------------------------------------------- (a) Initial speed is v = L1                               = (0.195 m)(4.8x105 rad/s)                                        = 0.936x105 m/s (b) Tangential acceelration is            a = L               = 0.07605 m/s2 (c) Radial acceleration is               ar = L2                  = 4.49x1010 m/s2                  = 4.49x1010 m/s2

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