Ahelicopter blade spins at exactly 100 revolutions per minute. its tip is 5.00 m from the center of rotation. (a) calculate the average speed of the blade tip in the helicopter's frame of reference. (b) what is its average velocity over one revolution?

a) 52.3 m/s

b) it has zero average velocity.

Explanation:

a) angular speed is the rate of change of the angle (in radians) with time. For this  case:

given: 1 revolution is equivalent to 2π radians

then: 100 revolutions are equivalent to 200π radians

angular speed = (200π rad)/ (60 s) = 10.46 rad/s

tangential speed is the speed of a point on the surface of the spinning object, which is the angular speed times the distance from the point to the axis of rotation. For this case:

tangential speed  = distance from tip to center * angular speed  

= 5 m * 10.46 rad/s = 52.3 m/s

b) The displacement made by the tip after one revolution is zero (its final position is equal to its initial position). Therefore, it has zero average velocity.

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