Question

A helicopter 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?

Answer 1

angular vel to tangential vel

v=r omega

v = 56 x 100/60 x 2 pi

v = 56x5/3x6

v=560m/s as estimate

100 revs, 5.00m

Answer 2

a) 52.3 m/s

b) it has zero average velocity.

Step-by-step 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.