4. When the little hand is on the 3 and the big hand is on the 12.. . .(Problem

Question

4. When the little hand is on the 3 and the big hand is on the 12.. . .(Problem 18) 19. BIO A centrifuge is a common laboratory instrument that sepa- rates components of differing densities in solution. This is accom- plished by spinning a sample around in a circle with a large angu- lar speed. Suppose that after a centrifuge in a medical laboratory is turned off, it continues to rotate with a constant angular decelera- tion for 10.2 s before coming to rest. (a) If its initial angular speed was 3850 rpm, what is the magnitude of its angular acceleration? (b) How many revolutions did the centrifuge complete after being turned off? 20. The Slowing Earth The Earth's rate of rotation is constantly decreasing causing the day to increase in duration. In the year

Explanation / Answer

Given Data

Initial speed i = 3850rpm ( 2 rad/60 s)

                       = 403.17 rad/s

the time taken to decelarate t = 10.2 s

the final angular speed f = 0

Solution:-

From rotational kinematics

     f = i +t

then angular acceleration

           = - i/t

              = - 403.17 / 10.2

              = - 39.53 rad/s^2

here negative sign indicates decelaration

The angular displacement

    f^2 = i^2 + 2

      = - i^2 / 2

         = -(403.17)^2 / 2(-39.53)

         = 2056.16 rad or 327.24 revolutions

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