1 A centrifuge is a common laboratory instrument that separa

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 19.2 s before coming to rest. (a) If its initial angular speed was 3650 rpm, what is the magnitude of its angular deceleration? (b) How many revolutions did the centrifuge complete after being turned off?

2. To balance a 35.5-kg automobile tire and wheel, a mechanic must place a 58.7-g lead weight 25.0 cm from the center of the wheel. When the wheel is balanced, its center of mass is exactly at the center of the wheel. How far from the center of the wheel was its center of mass before the lead weight was added?

Solution

1) o = 3650 rpm = 382.2 rad/s

Now = o + *t

        0 = 382.2 + *19.2 =======> = - 19.9 rad/s^2

ii) = 0.5*(o + )*t = 0.5*(382.2 + 0)*19.2 = 3669.12 rad = 584 rev

2) Moment is mass times distance. The moment of the weight is 58.7g x 25cm, or 1467.5 g cm (1.4675 Kg cm). The moment of the unbalanced wheel is therefore 1.4675Kg cm which is equal to the mass times distance. Algebra time!

1.4675Kg = 35.5Kg x distance

1.4675Kg/35.5Kg = distance

0.0413 cm = distance