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Angular acceleration, density question

  1. Feb 9, 2013 #1
    1. The problem statement, all variables and given/known data

    First question:
    "A DVD player can exert a torque on a DVD of 10−3 N⋅m. What is the DVD’s angular acceleration in rad/s2?

    Details and assumptions
    • The DVD has a mass of 0.015 kg and a radius of 0.06 m.
    • A DVD can be modeled as a thin uniform cylinder.
    "

    Second question:
    "A cube of ice 2 cm on a side is floating in a glass of water. You observe that the top of the ice is 0.166 cm above the surface of the water. What is the ratio of the density of ice to the density of water?"

    2. Relevant equations

    First question:
    α = [itex]\tau[/itex] / I
    I = Ʃmr2

    3. The attempt at a solution

    First question:
    α = 0.001 / ((0.015)(0.06)2)
    = 18.5185

    Not sure how I can do the second question at all...
    I've got these two questions from the internet.
    Please help me solve these question.
     
  2. jcsd
  3. Feb 10, 2013 #2

    haruspex

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    Yes, given the problem statement, but I'm astonished a DVD is to be modelled as a thin cylinder. A disc would be more reasonable, and that would change the answer.

    For the 2nd problem (in future, pls use separate threads for unrelated problems), what determines the volume of the ice that will be below water?
     
  4. Feb 10, 2013 #3
    α = 0.001 / ((0.015)(0.06)2)
    = 18.5185

    is not right...
     
  5. Feb 10, 2013 #4
    1. The moment of inertia of a disc or thin cylinder is

    I = 1/2 Mr2

    so you are out by a factor of 2.

    2. For this question you can start out with Archimedes' principle which states that the bouyant force on an object is equal to the weight of the liquid that it displaces.
     
  6. Feb 10, 2013 #5

    haruspex

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    For a disc, yes, but not for a thin cylinder about its axis. And it does say cylinder, strange though that is.
    Perhaps it meant short fat cylinder, but then why not just say disc?
     
  7. Feb 10, 2013 #6
    A thin solid cylinder would be a disc?
     
  8. Feb 10, 2013 #7
    Maybe I usually help 'too much'... :redface: To get started, think about the forces acting on the ice cube.
    ƩF=0 ⇔
    G=N...
     
  9. Feb 10, 2013 #8

    haruspex

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    It doesn't say solid, you've added that. The most obvious interpretation of 'thin cylinder' is that it is a tube with a thin wall, i.e. the cross-section has a narrow annulus. If it means thin the other way, why not say a very short solid cylinder, or even more naturally, a disc? But it is quite possible that the question is just very poorly worded.
     
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