Multiple-Concept Example 7 explores the approach taken in problems such as this

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 0.405 m and are rotating about a fixed axis with an angular velocity of +1.37 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of 1.88 rad/s2. After 0.495 s have elapsed since the switch was reset, what are the following? (See figure below.) the total acceleration (in m/s2) of a point on the tip of a blade 12.3 | ^ m/s2 the angle f between the total acceleration and the centripetal acceleration ac

Explanation / Answer

r=0.405m

w1=1.37rad/s

w2=1.88rad/s

t=0.495s

tangent acceleration a=r*(w2-21)/t= 0.495*(1.88-1.37)/0.495 =0.5099m/s^2

v2=r*w2 =0.405*1.88=0.7614m/s

centripetal acceleration= v^2/r =0.7614^2/0.405=1.4314m/s^2

Total acceleration: aT =sqrt(0.5099^2+1.4314^2) =1.5195m/s^2

angle = arctan(a/ac)=19.60degrees

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