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Calculate angular velocity of a ball rolling down incline?

  1. Apr 28, 2017 #1
    1. The problem statement, all variables and given/known data
    An 7.80-cm-diameter, 400 g solid sphere is released from rest at the top of a 1.70-m-long, 20.0 degree incline. It rolls, without slipping, to the bottom

    2. Relevant equations
    I=2/5 Mr^2
    K = 1/2 m*v^2
    Kroll = 1/2 Iw2
    mgh=K+Kroll
    3. The attempt at a solution
    Using the above energy equation and the fact that the ball is rolling without slipping I replaced v with 'rw' and then solved for w which gets me:
    w2 = (10gh)/(7r2)
    Where h is the height of the ramp. But I domt know what to do next. I tried finding h with trig and I got h=0.69
    but when I subbed those values in it was incorrect apparently. So the question is a little ambiguous when it says 'long' so I thought what if it means that is the length of the ramp itself which gets h=0.58 which is still wrong.

    I am taking the units to be rad/s and they actually matter for the answer if that is the problem.
     
  2. jcsd
  3. Apr 29, 2017 #2

    TSny

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    Homework Helper
    Gold Member

    Hello. Welcome to PF!
    OK
    I think this is the intended interpretation.
    Your outline of the solution looks correct to me. Sometimes there can be a careless error in substituting the numbers. You did not state the numerical value of your answer.
     
  4. Apr 29, 2017 #3
    So using that formula I get w=36.53rad/s
     
  5. Apr 29, 2017 #4
    Woops actually I get 79.69 because I forgot it is radius not diameter but that is still incorrect apparently
     
  6. Apr 29, 2017 #5

    gneill

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    Staff: Mentor

    You might be running into rounding or truncation issues affecting your significant figures. For example, if you truncate the change in height to two figures: h = 0.58 m, does it make any sense that anything calculated from that value could have more than two significant figures?

    Re-run your calculation keeping extra digits for all intermediate values (don't round anything until the very end) and see what you get. Use a value for g that has at least three significant figures.
     
  7. Apr 29, 2017 #6

    TSny

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    This answer corresponds to h = 0.69 m. What if you use h = .58 m? As gneill pointed out, your data is given to 3 significant figures, so you want your calculation to be accurate to the same number of significant figures.
     
  8. Apr 30, 2017 #7
    I think you should just try the math again. I ended up with the same final equation you did, plugged in the numbers, and got a different answer.
    I used
    g = 9.81m/s^2
    h = 0.5814 m
    r = 0.039 m

    Edit: Based on your previous posts, I suspect your radius may be wrong.
    Edit2: @TSny, you are probably right in post #6. I missed that when I posted.
     
    Last edited: Apr 30, 2017
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