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!

Projectile hits rod hanging from pivot.

  1. Dec 7, 2013 #1
    1. The problem statement, all variables and given/known data
    A thin, uniform bar, 2, long and weighing 90N is hanging vertically from the ceiling by a frictionless pivot. It is struck by a small 3kg ball, 1.5m below the ceiling, initially travelling horizontally at 10 m/s. The ball rebounds in the opposite direction with a speed of 6 m/s.

    2. Relevant equations

    Lbefore = Lafter

    L = Iω

    Irod = [itex]\frac{1}{2}[/itex]MR2

    Ipoint = MR2

    3. The attempt at a solution

    At the point of impact the ball can be thought of as a particle in circular motion about the pivot with radius 1.5m and tangential velocity 10m/s.
    The change in velocity is 16m/s. So the effective change in the angular momentum of the ball is

    ΔLball = Iball Δωball = [itex]\frac{IballΔv}{Rball}[/itex]

    This is equal to the change in the angular momentum of the rod (opposite direction):

    ΔLrod = Irod Δωrod = [itex]\frac{IballΔv}{Rball}[/itex]

    Insert values for I and rearrange :

    Δωrod = (2*mball*rball*Δvball) / (mrod*rball2)

    This gives ω = 3.92 rad/s , the given answer is 5.88 rad/s.
    Last edited: Dec 7, 2013
  2. jcsd
  3. Dec 7, 2013 #2
    I obviously used the fraction syntax incorrectly, please let me know what I did wrong. Thanks
  4. Dec 8, 2013 #3


    User Avatar
    Homework Helper

    The formula for the moment of inertia of the rod is not correct.

  5. Dec 8, 2013 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    itex gives up if you put non-itex codes like [s u b] inside. Use ^ for sup and _ for sub.
  6. Dec 8, 2013 #5


    User Avatar
    Homework Helper

    As haruspex said, _ for sub, but enclose subscript between curly thingies {} :smile:

    [itex]ΔL_{ball} = I_{ball} Δω_{ball} = \frac{I_{ball}Δv}{R_{ball}}[/itex]

    written as

    ΔL_{ball} = I_{ball} Δω_{ball} = \frac{I_{ball}Δv}{R_{ball}}

  7. Dec 8, 2013 #6
    Ah yes. I should stick to deriving the moments of inertia, my memory doesn't serve me well. Thanks.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted