Multiple-Concert Example 7 explores the approach taken in problems such as this
ID: 1463058 • Letter: M
Question
Multiple-Concert Example 7 explores the approach taken in problems such as this one. The blades of a ceiling fan have a radius of 0.344 m and are rotating about a fixed axis with an angular velocity of + 1.71 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of + 2.40 rad/s^2. After 0.684 s have elapsed since the switch was reset, what is (a) 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 and the centripetal acceleration (See Figure b)?Explanation / Answer
a)
1st calculate angular acceleration ar,
use:
wf = wi + ar*t
2.4 = 1.71 + ar*0.684
ar= 1 rad/s^2
aT = r*ar = 0.344 * 1 = 0.344 m/s^2
ac = r*wf^2 = 0.344*(2.4)^2 = 1.98 m/s^2
total acceleration, a = sqrt (aT^2 + ac^2) = sqrt (0.344^2 + 1.98^2) = 2 m/s^2
b)
angle= atan (aT/ac) = atan (0.344/1.98) = 9.9 degree
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