A swinging bucket centrifuge spins its test-tubes around a central axis. When they start,
they are in their normal, upright position, but then they swing base-outward as the
centrifuge rotates, as shown in the figures at right. Of course, the test-tubes are
contained in housings, often aluminum. Consider such a centrifuge that holds 4 tubes.
When they are spinning, the bottom of the rotor+tubes is 18.5 cm from the axis. Suppose
each tube and aluminum housing has a mass of 1.5 kg and the central part is negligible.
When the tubes are extended, you may consider them as solid rods going all the way to
the central axis for purposes of this problem. This centrifuge is spinning at 7500 rpm.
(A) What is the moment of inertia of the entire centrifuge rotor?
(B) What is its rotational kinetic energy?
(C) What is the speed of the tip of the test tube?
(D) What is the acceleration of the test tube in g's?
A piece of mass 2.7 grams breaks off the end of the tube while it is rotating.
(E) How much kinetic energy does it have as it flies toward the wall?