A ceiling fan with 89-cm-diameter blades is turning at 64 rpm .?

Suppose the fan coasts to a stop 25 seconds after being turned off.

a) What is the speed of the tip of a blade 10 seconds after the fan is turned off?

b) Through how many revolutions does the fan turn while stopping?

2 Answers

  • r = 0.89/2m= 0.445m;

    t =25; v=0; u=64 rpm = 64* 2*pi /60 = 6.7 rad/s

    v =u+at

    0 = 6.7 + 25 a

    a = - 0.268 rad/s2

    a) v = u +at

    v = 6.7 - 0.268 * 10

    v = 4.02 rad/s

    speed of the tip of a blade = 0.445 * 4.02 = 1.789m/s --answer

    b) s = ut + 0.5 at^2

    s = 6.7 * 25 - 0.5 * 0.268* 25^2

    s = 83.75rad

    = 13.33 rev

    answer

    revolutions the fan turned while stopping

  • It depends on whether the fan is decelerating at a constant rate.

    "Coasts" is a very vague term.

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