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 0.376 m and are rotating about a fixed axis with an angular velocity of +1.19 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of +2.96 rad/s2. After 0.488 s have elapsed since the switch was reset, what is (a) the total acceleration (in m/s2) of a point on the tip of a blade and (b) the angle o between the total acceleration a and the centripetal acceleration a, (see Figure b)?

Answer 1

a) re 0.376 m W . = 1:19 rad/s. X: 2.96 rad/sa t = 0.488 sec _ . Wp = 0); + at = 1.19 + 2-96%0.488 _ W ,! 2.63448 radlo :: a & Q = : rdo 0.376 x 2.96 = '1.11286 m/s2 r we ? = 0.376 (2-63448) :. ac = 2.60962 m/s2 . Totat acceleration is given by - a -1 242 +ąż = V(1.11296)2+ (2.60962)2 | a = 2.837 m/s2|| | 6) & tant ( at ) tant (111296) De tant(0.4264835493) tant0.426483 - Þ - 23.10