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Rotational motion

  1. Jul 12, 2015 #1
    1. A ring , a disk and a sphere all of same mass and radius, with moments of inertia Ir, Id, Is respectively about their axes, roll down without slipping on an inclined plane from a given height. If the time taken for the ring, disk and sphere to reach the bottom of the plane are tr, td and ts respectively, then
    1)tr<td<ts
    2)tr=td=ts
    3)tr>td>ts
    4)tr>td=ts
    5)tr>td<ts

    2. Relevant equations
    . torque=moment of inertia*angular acceleration


    3. The attempt at a solution
    I took the torque acting on the objects to be the same theefore moment of inertia to be indirectly proportional to angular acc.

    Ir>Id>Is
    therefore:
    tr<td<ts

    If anyone show where I went wrong, it'll be of great help.
     
  2. jcsd
  3. Jul 12, 2015 #2

    CWatters

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    Can you explain? The moment of inertia of an object is normally a constant that depends on the objects shape (among other things). For example if you spin up a flywheel it's moment of inertia doesn't change.
     
  4. Jul 12, 2015 #3
    Since the radii of the objects are equal and their masses are equal, i took the torque acting on them to be equal.
     
  5. Jul 12, 2015 #4
    therefore considering torque= I * Angular acc. , I took angular acc is indirectly proportional to I
     
  6. Jul 12, 2015 #5
    I think you meant to say "inversely proportional".

    So if the accelerations are smaller for larger moments of inertia, what does that do to the time?
     
  7. Jul 12, 2015 #6
    oh.. Stupid me.. Smaller accelerations means longer time.. Thank you very much!!
     
  8. Jul 12, 2015 #7

    CWatters

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  9. Jul 12, 2015 #8
  10. Jul 12, 2015 #9
    Thank you very much!!
     
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