<p>Multiple-Concept Example 7 explores the approach taken in problems such as th

Question

<p>Multiple-Concept Example 7 explores the approach taken in problems such as this one.&#160; The blades of a ceiling fan have a radius of 0.380 m and are rotating about a fixed axis with an angular velocity of +1.50 rad/s.&#160; When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of +2.00 rad/s^2.&#160; After 0.500 s have elapsed since the switch was reset, what is (a) the total acceleration (in m/s^2) of a point on the tip of a blade and (b) the angle&#160; &#966; between the total acceleration and the centripetal acceleration?&#160; ( See Figure 8.12 b.)</p>

Explanation / Answer

The blades of a cieling fan having radius r = 0.380m Rotating about a fixed axis with angular velocity = 1.50 rad /s The blades a cquire an angular acceleration = + 2.00 rad /s^2 a ) velocity v = r                         = 0.380m * 1.50 rad /s                         = 0.57 m/s centripetal acceleration a_c = v^2 / r                                              = (0.57 m/s)^2 / 0.380 m                                              = 0.855 m/s^2 tangential acceleration is a_t = r                                               = 0.380m * 2.00rad /s^2                                               = 0.76 m/s^2 total acceleration is a = ( 0.855)^2 + ( 0.76)^2                                       = 1.14 m/s^2 b )   angle between the total acceleration and centripetal acceleration is                               = tan ^-1 ( 1.14 / 0.855)                                   = 53 degrees

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