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 5.00 x 105 rad/s and the driving force is turned off, its spinning slows down at an angular rate of magnitude 0.400 rad/s. The rotor of the Beams ultracentrifuge is a rod 38.2 cm long, turning about a perpendicular axis through its center. Problem 05.054.a - Initial speed For a point at the end of the rotor, find the initial speed. 190000 m/s

Answer 1

Initial angular speed, ω = 5.0 x 10^5 rad/s

Radius of the centrifuge = length of the rod = r = 38.2 cm = 0.382 m

(a) Initial speed, v = r*ω

= 0.382 m x 5.0 x 10^5 rad/s

= 1.91 x 10^5 m/s (Answer)

(b) Tangential acceleration component, a(tan) = r*α

= 0.382 m*(-0.40 rad/s^2) = -0.1528 m/s^2 (Answer)

(c) Maximum radial acceleration component, a(rad) = r*ω^2

= 0.382 m*(5.0x10^5 rad/s)^2

= 9.55 x 10^10 m/s^2 (Answer)