In a Beams ultracentrifuge, a 20.1 cm long rotor is suspended magnetically in a

Question

In a Beams ultracentrifuge, a 20.1 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.105 m/s

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

(c) For a point at the end of the rotor, find the maximum radial acceleration component.
m/s2

Explanation / Answer

Assuming 105 means 105:

part (a):   v = r = (4.8 * 105 s-1)(0.201 m) = 9.65 * 104 m/s = 0.965 * 105 m/s

part (b):   atan = r = (0.39 s-2)(0.201 m) = 0.0784 m/s2

part (c):   arad = v2/r = (9.65 * 104 m/s)2/(0.201 m) = 4.63 * 1010 m/s2

Part c is the acceleration value right after the driving force is turned off; as the beam slows down it will very gradually decrease; so this answer is the maximum.

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