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 0.399 m and are rotating about a fixed axis with an angular velocity of +1.61 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of 1.82 rad/s2. After 0.465 s have elapsed since the switch was reset, what are the following? (See figure below.) (a) the total acceleration (in m/s2) of a point on the tip of a blade m/s2 (b) the angle between the total acceleration and the centripetal acceleration ac

Explanation / Answer

a) total acceleration = sqrt(((1.61 + 1.82*0.465)^2*0.399)^2 + (1.61*0.399)^2) = 2.51 m/s2 b) angle = taninverse(1.82/(1.61+1.82*0.465)^2) = 16.8 degrees

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