
DYNAMICS  CASE STUDY



Introduction

Problem Diagram 

An oscillating fan is rotating about a vertical axis. An unsuspecting fly flies into the fan and hits the tip of one of the blades when the blade is in the vertical position. What will happen to the fly?
What is known:
 At the instant the fly hits the fan, the fan is rotating about the vertical axis with an angular speed of Ω_{f} = 0.296 rad/s, increasing at a rate of dΩ_{f}/dt = 0.0419 rad/s^{2}.
 The blades of the fan are spinning at a constant rate of ω_{b} = 2π rad/s.
 The fan has the dimensions shown, and is rotated 15° up from horizontal.


Question


At the instant the fly hits the fan, what are the velocity and acceleration of the tip (point B) of the vertical (uppermost) blade? 



Approach


 Consider a coordinate system, located at the center of the blades, that rotates with the fan.
 Use equations of motion in three dimensions for a translatingrotating coordinate system.
 Only consider the instant in time when the fly hits the fan.




