1) A centrifuge is a common laboratory instrument that separates components of d

Question

1) A centrifuge is a common laboratory instrument that separates components of differing densities in solution. This is accomplished by spinning a sample around in a circle with a large angular speed. Suppose that after a centrifuge in a medical laboratory is turned off, it continues to rotate with a constant angular deceleration for 10.2 s before coming to rest.

a) If its initial angular speed was 3880 rpm , what is the magnitude of its angular deceleration? Please give your answer in rev/s2

b) How many revolutions did the centrifuge complete after being turned off? Please give your answer in rev

2) The drill used by most dentists today is powered by a small air-turbine that can operate at angular speeds of 350000 rpm. These drills, along with ultrasonic dental drills, are the fastest turbines in the world-far exceeding the angular speeds of jet engines. Suppose a drill starts at rest and comes up to operating speed in 2.1 s. Find the angular acceleration produced by the drill, assuming it to be constant. Please give your answer in rev/s2.

Explanation / Answer

1 a) frequency =3880/60=64.67s-1

angular velocity =2¶64.67=406.31rad/s

time=10.2s

angular decleration=406.31/10.2=39.83rad/s^2=6.34revolution/s2

No. of revolutions = 406.31*406.31/2*39.83*2¶=329.83revolutions

2. time=2.1s

angular speed=2¶350000/60=36651.9rad/s

angular acceleration=36651.9/2.1=17453.28rad/sec2

angular acceleration=17453.28/2¶=2777.78revolutions/sec2

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