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Radial and Transverse Acceleration

  1. Jan 30, 2013 #1
    1. The problem statement, all variables and given/known data

    Three stock car drivers are racing around a circular bend. They are each circling the bend at different radii: r1=249 m, r2=255 m, and r3=261 m. At a given instant, all three are traveling at the same transverse rate of rotation, [itex]\dot{\theta}[/itex]1=[itex]\dot{\theta}[/itex]2=[itex]\dot{\theta}[/itex]3=0.271 [itex]\frac{rad}{s}[/itex] .The cars are also increasing their transverse rate of rotation by the same rate, [itex]\ddot{\theta}[/itex]1=[itex]\ddot{\theta}[/itex]2=[itex]\ddot{\theta}[/itex]3=2.71×10-2[itex]\frac{rad}{s^2}[/itex].Determine the magnitudes of the velocity and acceleration of the first driver.

    2. Relevant equations

    a=√ar2+a[itex]\theta[/itex]2

    ar=[itex]\ddot{r}[/itex] - r[itex]\dot{\theta}[/itex]2

    aθ=r[itex]\ddot{\theta}[/itex] + 2[itex]\dot{r}[/itex][itex]\dot{\theta}[/itex]

    3. The attempt at a solution

    ar=18.286809 [itex]\frac{rad}{s^2}[/itex]
    aθ=6.7479 [itex]\frac{rad}{s^2}[/itex]
    a=√18.2868092 + 6.74792 = 19.492 [itex]\frac{rad}{s^2}[/itex]

    v = ??

    I'm not sure if the velocity is 18.286809 [itex]\frac{rad}{s^2}[/itex] or not?
     
    Last edited: Jan 30, 2013
  2. jcsd
  3. Jan 30, 2013 #2

    mfb

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    Staff: Mentor

    I would calculate this in cartesian coordinates.
    And rad/s^2 as unit does not make sense for the magnitude of an acceleration.

    If you travel in a circle with a radius of 249m with an angular velocity of 0.271 rad/s, what is your velocity? Hint: It is a very easy formula.
     
  4. Jan 30, 2013 #3
    Is this the answer:

    v = w*r
    = 0.271 rad/s * 249m
    = 67.48m/s
     
  5. Jan 30, 2013 #4

    mfb

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    Staff: Mentor

    That is right.
     
  6. Jan 30, 2013 #5
    I see. I didn't find this in my textbook, "Engineering Mechanics: Dynamics" by Hibbeler. I'll have to remember this.

    Thanks for your help!!
     
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