Multiple-Concept Example 7 explores the approach taken in problems such as this
ID: 1440529 • Letter: M
Question
Multiple-Concept Example 7 explores the approach taken in problems such as this one. The blades of a ceiling fan have a radius of 0.337 m and are rotating about a fixed axis with an angular velocity of +1.22 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of +1.40 rad/s^2. After 0.341 s have elapsed since the switch was reset, what is (the total acceleration (in m/s^2) of a point on the tip of a blade and (b) the angle phi between the total acceleration a and the centripetal acceleration a_c (See Figure 8.13b)?Explanation / Answer
r =0.337 m , w =1.22 rad/s, alpha =1.4 rad/s^2, t =0.34 s
(a) tangental acceleration at = r*alpha = 0.337*1.4 = 0.4718 m/s^2
From rotational kinematic equation w =wo +aplha*t
w = 1.22+ (1.4*0.341) = 1.6974 rad/s
radial acceleration ar = w^r = 1.6974*1.6974*0.337
ar = 0.97 m/s^2
Totla acceleration = ((0.4718)^2+(0.97)^2)^0.5
a = 1.08 m/s^2
(b) tan(phi)= ac/a = 0.97/1.08
phi = 42 degrees
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