A fan rotating with an initial angular velocity of 1000 rev/min is switched off.

Question

A fan rotating with an initial angular velocity of 1000 rev/min is switched off. In 2 seconds, the angular velocity decreases to 200 rev/min. Assuming the angular acceleration is constant, how many revolutions does the blade undergo during this time? A ball attached to a string starts at rest and undergoes a constant angular acceleration as it travels in a horizontal circle of radius 0.30 m. After 0.65 sec, the angular speed of the ball is 9.7 rad/s. What is the tangential acceleration of the ball?

Explanation / Answer

1)   here, angular deacceleration = (1000 - 200) * 60/2

                                                      = 24000 rev/min2

=> revolutions blade undergo =   1000 * (2/60) - 1/2 * 24000 * (2/60) * (2/60)

                                                 =   20 revolutions

2) angular acceleration = 9.7/0.65 = 14.92 rad/sec2

=> tangential acceleration of ball = 14.92 * 0.30

                                                   = 4.476   m/sec2

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