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 0.327 m and are rotating about a fixed axis with an angular velocity of +1.27 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of +1.12 rad/s2. After 0.551 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 between the total acceleration and the centripetal acceleration (See Figure 8.13b)?

Explanation / Answer

r= 0.327 W= 1.27 ang accn = 1.12 t= 0.551 W= Wo + ang accn t= 1.27 + 0.551 X 1.12 = 1.887 rad/s now, velocity of the point on the = WR = 0.617 accn = 1.22 m/s^2 angle = tan-1( 1.16 / 0.366) = 72.48 degrees.

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