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Centripetal acceleration and tangential acceleration

  1. May 23, 2014 #1
    When having a circular acceleration motion, we have both tangential acceleration and centripetal acceleration.

    The tangential acceleration is aT=r*α where α=1/2*(ωf0). So we can see tha aT is dependant on both the initial angular velocity ω0 and the final ωf).

    For centripetal acceleration, we instead have aC=r*ωf2.

    My question is, how come the centripetal acceleration is only dependant on the final angular velocity, and not the initial?
    Is there a physical explanation for this?
     
  2. jcsd
  3. May 23, 2014 #2
    First: α isn't 1/2*(ωf0). The correct equation is α = (ωf0)/(tf-t0).

    Second: The equation above is the expression for the AVERAGE angular acceleration. If the circular motion is UNIFORMLY accelerated than you can use the average angular acceleration to calculate the tangential speed since angular acceleration is constant, otherwise you have to use the instantaneous angular acceleration - say αf and the expression for tangetial acceleration becomes aTf = r αf
     
  4. May 23, 2014 #3
    Ok thanks for the correction. But I still wonder why the centripetal acceleration is only dependant on the final angular velocity, and not the initial angular velocity. Is there a physical explanation for this?
     
  5. May 23, 2014 #4
    centripetal acceleration is caused to continue circular motion so at every point. so at that point it has to accelerate the mass toward center so as to change it direction.
    now for at the point it has angular velocity omega then centripetal acceleration will vary with that only
     
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