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Falling rotating sphere and displacements

  1. Mar 30, 2016 #1
    1. The problem statement, all variables and given/known data
    proxy.php?image=http%3A%2F%2Fi.imgur.com%2FN04l7ru.png

    2. Relevant equations
    How to locate the point P and C after 0.5s from their initial position ?
    3. The attempt at a solution
    Well i don't know whether it would be correct way to start the problem i.e find the centripetal acceleration .
     
  2. jcsd
  3. Mar 30, 2016 #2

    Merlin3189

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    You can find how far C moves in 0.5 sec, since it is the centre of gravity of the sphere.
    So you know the two positions of the sphere and where P is at each position.
    Then simply work out PP' and CC' and find the ratio.
     
  4. Mar 30, 2016 #3
    To compute for the displacement of point C use the equation for free falling bodies. As for point P, compute for the angle using the angular velocity and you will find that it has traveled all the way to the other side of the sphere (be careful here as you are dealing with displacement, not total distance). With that you should be able to get the ratio.
     
  5. Mar 30, 2016 #4
    As C is in free fall condition,so
    0Vs5NZr.png
    How to find angle using angular velocity ?
     
  6. Mar 30, 2016 #5

    Merlin3189

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    distance = velocity x time so angle = angular velocity x time

    You can work that out from the question, because the angular velocity is given as radians per second. So if you multiply it by seconds, you will get radians.

    PS. They've given a really easy angular velocity.
     
  7. Mar 30, 2016 #6
    i got π radians.
    So, displacement of point P would be 2r=1.25 m
     
  8. Mar 30, 2016 #7
  9. Mar 30, 2016 #8
  10. Mar 30, 2016 #9

    Merlin3189

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    I think you're forgetting that as P rotates round the sphere, the whole sphere is moving down.
    If the sphere were not rotating, P would move the same distance as C (1:1), but the rotation adds to the displacement of P.
     
  11. Mar 30, 2016 #10
    Okay.
    So answer would be 2:1.
     
  12. Mar 30, 2016 #11
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