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Banked curve

  1. Mar 28, 2016 #1
    1. The problem statement, all variables and given/known data
    Imagine another planet with an acceleration of 10.00 m/s^2 at its equator when ignoring the rotation of the planet. The radius is 6.2 x10^6 m. An object dropped at the equator yields an acceleration of 9.70 m/s^2. Determine the length of 1 day on this planet.



    2. Relevant equations


    3. The attempt at a solution
    My teacher taught me how to solve this question, but there is just one step I don't understand
    10.00m/s^2 - 9.70m/s^2 = 0.3m/s^2 (centripetal acceleration)
    why does subtracting these two values give us the centripetal acceleration??
    On a test, if I get a similar question I know I have to subtract the two values, but I really want to learn the reason behind it.
     
  2. jcsd
  3. Mar 28, 2016 #2

    andrewkirk

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    Do you know how to derive the formula for centripetal acceleration in terms of velocity, using a vector triangle showing the change in velocity over a small increment of time ##\delta t##? A similar construction can be used to justify the above formula. There's a ##\cos\delta\theta## factor in there that is approximated by 1 to get the above formula.
     
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