Question

A rotating fan completes 1160 revolutions every minute. Consider the tip of a blade, at a radius of 17.0 cm. (a) Through what distance does the tip move in one revolution? What are (b) the tip's speed and (c) the magnitude of its acceleration? (d) What is the period of the motion?

Answer 1

  Given Data

    angular velocity, ω = 1160 rev /m

                               = [1160* (2π) /60 ] = 121.5 rad/s

        radius r = 17 cm = 0.17 m

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   a)   The distance travelled is , d = 2πr

                   = 2π(0.17 m)

                                                  = 1.07 m

   b) The tip's speed is

            v = rω

             = 0.17*121.5

            = 20.65 m/s

c) ) the magnitude of its acceleration is given by

             a = v² /r

                = 20.65² / 0.17

                = 2508.55 m/s²

d)  the period of the motion is givenby

                   T = 2π /ω

                   T = 2π /121.5

                   T = 0.052 s