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Angular acceleration and angular velocity

  1. Apr 14, 2012 #1
    1. The problem statement, all variables and given/known data

    Calculate the angular acceleration and angular velocity of a 4 kg object rotating in a circle of 3 m radius in a time of 6 s.


    2. Relevant equations

    Angular acceleration = ω2*r

    Angular velocity= angular displacement/time ????


    3. The attempt at a solution

    Really don't know how to start :C
     
  2. jcsd
  3. Apr 14, 2012 #2

    BruceW

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    hmm. It might help if you went over some of the topics of circular motion. Also, the question is badly worded or incomplete? Angular acceleration is a term usually used for the acceleration which is perpendicular to the radial motion. So it is not omega squared times r. The radial acceleration is usually used for omega squared times r.

    But with what the question gives you, it looks like the angular acceleration cannot be found, although the radial acceleration can. So I think you can assume you are meant to work out the radial acceleration.

    Another problem with the question is that it doesn't explicitly say how far the object moves in that 6 seconds. But at a first guess, I'd say you are meant to assume it completes one full rotation in 6 seconds.

    So, assuming the object completes one full rotation in 6 seconds, then what is the angular velocity? You've written the equation: "Angular velocity= angular displacement/time" so what is the 'angular displacement' for one full rotation?
     
  4. Apr 16, 2012 #3
    My calculation looks like that

    Angular velocity:

    360/57.3=6.28 rad/s

    6.28 rad/s / 6= 1.04 rad/sec


    but what about angular acceleration?

    Am I right i thinking?
     
  5. Apr 16, 2012 #4
    The time period is given to you as 6 seconds.
    You need ##\omega## (angular velocity).

    ##Period = \frac{2 \pi}{\omega}##

    For, angular acceleration, I think the data is incomplete because angular acceleration ##\alpha=\frac{d\omega}{dt}##. So you need more values.
     
  6. Apr 18, 2012 #5

    BruceW

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    Yep, this is right. (Although, it is 6.28 rad, and it only gets the units of rad/sec when you divide by time). The question asks about angular acceleration, but as warlock says, the angular acceleration cannot be found. So it is more likely that the question meant radial acceleration (aka centripetal acceleration). And you do have the correct equation for this.
     
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