Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to deal with direction on impluse?

  1. Dec 31, 2008 #1


    User Avatar

    I am using impulse-momentum theorem in problem solving. But I am quite confusing about deal with the direction of momentum so always get the wrong sign.

    For example, assume a long thin bar with mass M and length L hanging from a fixed frictionless point A at the ceiling, the bar is stay at rest. Now a bullet with mass m and initial velocity [tex]v_0[/tex] moving horizontally towards the bar and hit it at point B (the distance b/w A and B is y). Finally, the bullet embed into bar and then moving together with it. The instantaneous horizontal impulse when it hit the bar is [tex]I_b[/tex], find the intial angular velocity of the bar.

    Since the system's total momentum is conserved, we can write

    mv_0 = (m+M)V_f

    and the change of the momentum of the bullet is the impulse

    MV_f = -m(v_f-v_0) = -I_b

    then the initial angular momentum of bar can be given by

    L = MV_f y = -I_b y

    After collision, the bar (and the bullet) move around pivot A, the moment of inertia about A is [tex]I=ML^2/3[/tex] (ignore the mass of bullet). With the help of following equation

    [tex]L = I\omega[/tex]

    we find that

    [tex]\omega = \frac{L}{I} = - \frac{3I_b y}{ML^2}[/tex]

    the result (the value) is correct, but it should be positive. I have no idea where is the mistake come from.
  2. jcsd
  3. Dec 31, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Since the impulse on the bullet is negative, it follows from Newton 3 that the impulse on the rod must be equal but opposite, that is, positive. Bottom line, however, is that whether one calls [tex] \omega [/tex] positive or negative, it's rather a question as to whether the rotation is clockwise or counterclockwise. The sign choice is largely a matter of convention.
  4. Dec 31, 2008 #3


    User Avatar

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook