Many problems involve only linear velocities, which have relatively simple mathe

Question

Many problems involve only linear velocities, which have relatively simple mathematical descriptions. In circular motion, the linear velocity is constantly changing direction, so the mathematics becomes complicated in Cartesian coordinates. The velocity and position vectors are perpendicular to each other. The math becomes much simpler if we use polar coordinates and look at the angular velocity. (Figure 1)

Polar coordinates (r,) refer to the angular position and the distance from the origin r. If the angular velocity is constant, then it equals the change in angular position divided by the change in time: =t. From the angular velocity and the radius of the circle, the linear speed of an object can be found.

A) The tips of the blades of the Chinook helicopter lie on a circle of diameter of 18.29 meters. What is the airspeed v of the tip of the blades when they are rotating at 225 rpm?

B)

Consider the part of a blade that is 4.00 meters from the central hub. What is the velocity v of this part when the blades are rotating at 225 rpm?

Explanation / Answer

A) angular speed, w = 225 rpm

= 225*2*pi/60 rad/s

= 23.55 rad/s

radius of the blade, R = d/2

= 18.29/2

= 9.145 m

Apply, v = R*w

= 9.145*23.55

= 215.4 m/s

B) Again use, v = r*w

= 4*23.55

= 94.2 m/s

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