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Rotational Kinetics hardest problem

  1. Oct 22, 2006 #1
    Multiple-Concept Example 7 explores the approach taken in problems such as this one. The blades of a ceiling fan have a radius of 0.375 m and are rotating about a fixed axis with an angular velocity of +1.95 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of +2.69 rad/s2. After 0.473 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)?

    I am very lost on this problem.

    THe example pretty much just told me that

    a = Sqrt ac^2 + aT^2

    I have no clue how to begin this problem. please help even if its just a hint.

    THanks
     
  2. jcsd
  3. Oct 22, 2006 #2

    OlderDan

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    We are going to have to agree on an interpretation of the given information. I assume they mean the the tips of the blades of the fan are .375m from the center of the axis or rotation. Lets just call that R. There is a connection between the angular velocity of the blades, and the speed that a blade tip is moving. Since there is an angular acceleration for some period of time, the angular velocity will be increasing and will reach a new value at the end of the specified time. At that time, the blade tip speed is still increasing, but has a new value that can be calculated from the given information.

    At the point in question the blade tip has both a speed and a rate of change of speed. The speed has an associated centripetal acceleration directed toward the center of the circle. The rate of change of speed has an associated acceleration in a direction tangent to the circle. Your job, should you choose to accept it, is to find these two components of acceleration and their resultant and find the angle between the total acceleration and the centripetal component.
     
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