1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What fraction of its total kinetic energy is rotational kinetic energy

  1. Nov 23, 2013 #1
    1. The problem statement, all variables and given/known data
    A spherical object with moment of inertia 0.57mr2 rolls without slipping down an incline. At the bottom of the incline.


    2. Relevant equations
    For a sphere (or cylinder) rolling without slipping ω = v/r.

    Rotational KE = ½Iω²

    The translational kinetic energy = ½mv²

    3. The attempt at a solution
    Rotational KE = ½Iω²
    = ½ * 0.57mr² (v/r)²
    = 0.285mv²

    The total kinetic energy = 0.285mv² + ½mv² = 0.785mv²

    Rotational kinetic energy as a fraction of the total energy is:
    (0.285mv²) / (0.785mv²) = 0.363

    the question asked to answer in percentage so would it be 36.3%
     
  2. jcsd
  3. Nov 23, 2013 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

  4. Nov 25, 2014 #3
    HI I'm trying to work out the same problem but I dont get where the total kinetic energy = 0.285mv² + ½mv² = 0.785mv²
     
  5. Nov 25, 2014 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    What's the linear KE in terms of m and v? What's the rotational KE in terms of I and ##\omega##? What is the relationship between v, r and ##\omega##?
     
  6. Nov 25, 2014 #5
    liner KE in terms of m and v would be 1/2mv^2, rotational KE in terms of 1/2Iω^2, and I know that v= ωr
     
  7. Nov 25, 2014 #6

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    And you know I here in terms of m and r. Substitute to find rotational KE in terms of m and v.
     
  8. Nov 25, 2014 #7
    Rotational KE = ½Iω²
    In my problem moment of inertia 0.6mr^2
    = 1/2 * 0.6mr^2 (v/r)^2
    = 0.3mv^2
     
  9. Nov 25, 2014 #8

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    OK, so what's the total KE in terms of m and v? What fraction of that is rotational?
     
  10. Nov 25, 2014 #9
    This is where I get lost, I understand that total KE is 1/2mv^2+.3mr^2
     
  11. Nov 25, 2014 #10

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    No, the .3mr^2 is wrong. Go through the steps again carefully. If you still get that, please post all steps.
    (The .3 is right, it's the mr^2 bit)
     
    Last edited: Nov 25, 2014
  12. Nov 25, 2014 #11
    1. The problem statement, all variables and given/known data
    A spherical object with moment of inertia 0.6mr2 rolls without slipping down an incline. At the bottom of the incline.

    2. Relevant equations
    Rotational KE = ½Iω²
    The translational kinetic energy = ½mv²

    3. The attempt at a solution
    Rotational KE = ½Iω²
    = ½ * 0.6mr² (v/r)²
    = 0.3mv²

    The total kinetic energy = 0.3mv² + ½mv²
     
  13. Nov 25, 2014 #12

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Right. So what fraction of that is rotational?
     
  14. Nov 25, 2014 #13
  15. Nov 25, 2014 #14

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    No.
    Simplify that to get the total KE.
     
  16. Nov 25, 2014 #15
    total KE = 0.8mv²
     
  17. Nov 25, 2014 #16

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Right. What fraction is 0.3mv² of that?
     
  18. Nov 25, 2014 #17
    0.375
     
  19. Nov 25, 2014 #18

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Er.. no. How did you get that?
     
  20. Nov 25, 2014 #19
    sorry I meant .375
     
  21. Nov 25, 2014 #20

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Right.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: What fraction of its total kinetic energy is rotational kinetic energy
  1. Total kinetic Energy (Replies: 1)

Loading...