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Hollow sphere, angular momentum, torque problem? help?

  1. Nov 16, 2012 #1
    Hollow sphere, angular momentum, torque problem? help??

    a hollow sphere or radius 0.15m with rotational inertia = 0.040 kg m^2 about a line through its center of mass, rolls without slipping up a surface inclined 30 degree to the horizontal. at a certain initial position,the sphere's total kinetic energy is 20J.

    a) How much of this initial KE is rotational?




    what i did

    Hollow sphere = 2/3MR^(2)
    KErot = 1/2 Iω^2

    KEtotal = KEtranslational + KErotational

    a) 20 = 1/2mv^2 + 1/2 x 2/3 mr^2
    20 = 1/2mv^2 + 1/3 mr^2

    this part confuses me
    1/2mv^2 + 1/3 mr^2 = 5/6mv^2
    20 = 5/6mv^2

    How was 1/2mv^2 + 1/3 MR^2 = 5/6mv^2?? mv and MR are different yet how were they both added together??
     
  2. jcsd
  3. Nov 16, 2012 #2

    haruspex

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    Re: Hollow sphere, angular momentum, torque problem? help??

    When dimensions don't match up, backtrack to the first instance. It's here:
    ω is missing.
     
  4. Nov 17, 2012 #3
    Re: Hollow sphere, angular momentum, torque problem? help??

    1/2mv^2 + 1/2 x 2/3 mr^2ω = 5/6mv^2

    ok so if i put a ω there, how would it still = 5/6mv^2? in other words how can you change mr^2ω into mv^2? help!!
     
  5. Nov 17, 2012 #4
    Re: Hollow sphere, angular momentum, torque problem? help??

    oh nvm i got it. w = V^2/R^2. r cancel out. thanks!
     
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