Multiple-Concept Example 7 explores the approach taken in problems such as this
ID: 2024388 • Letter: M
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 0.335 m and are rotating about a fixed axis with an angular velocity of +1.12 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of +2.90 rad/s2. After 0.652 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
Given Radius of the ceiling fan, r = 0.335 m Angular velocity of the blade, = 1.12 rad/s Angular acceleration , = 2.90 rad/s^2 Time interval , t = 0.652 s (a) Total acceleration, aT = (ac)2 +(at)2 Centripetal acceleration is, ac = r 2 = (0.335 m) (1.12 rad/s)2 = 0.42 m/s^2 Tangential acceleration is, at = r = (0.335 m) (2.90 rad/s^2) = 0.97 m/s^2 Total acceleration, a = (0.42 m/s^2)^2 + (0.97 m/s^2)^2 = 1.06 m/s^2 --------------------------------------------------------------------- (b) Angle between total acceleration and centripetal acceleration is, = cos^-1( ac/ a) = cos^-1((0.42 m/s^2) /(1.06 m/s^2)) = 66.65^0 --------------------------------------------------------------------- (b) Angle between total acceleration and centripetal acceleration is, = cos^-1( ac/ a) = cos^-1((0.42 m/s^2) /(1.06 m/s^2)) = 66.65^0Related Questions
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